Assertion-Reasoning Type Questions

Assertion (A): When a beam is in static equilibrium, the sum of clockwise moments is equal to the sum of anticlockwise moments.

Reason (R): According to the principle of moments for a body in equilibrium, the sum of moments acting in one direction must be equal to the sum of moments in opposite direction.

1. Both A and R are true.
2. Both A and R are false.
3. A is false but R is true.
4. A is true but R is false.

Answer

Both A and R are true.

Explanation

Assertion (A) is true because when the sum of the clockwise moments acting on the beam is equal to the sum of the anticlockwise moments, their resultant sum is zero and the beam has no rotational motion. Hence, it is in static equilibrium.

Reason (R) is true because it provides a logical explanation for Assertion (A), stating the principle of moments for a body in equilibrium, which aligns with the definition of static equilibrium.

Assertion (A): A heavier object placed at a far distance from the pivot point will have the same moment as a lighter object placed close to the pivot point.

Reason (R): The moment of force is determined by the magnitude of the force along with its distance from the pivot point.

1. Both A and R are true.
2. Both A and R are false.
3. A is false but R is true.
4. A is true but R is false.

Answer

A is false but R is true.

Explanation

The moment of a force is equal to the product of the magnitude of the force and the perpendicular distance of the line of action of the force from the axis of rotation. Hence, a heavier object placed at a far distance from the pivot point will have a greater moment than a lighter object placed close to the pivot point. Therefore, Assertion (A) is false.

Reason (R) is true. The moment of force is determined by the magnitude of the force along with its distance from the pivot point.

Assertion (A): The centre of gravity of an irregularly-shaped object always lies at its geometric centre.

Reason (R): The centre of gravity depends on the distribution of mass within an object.

1. Both A and R are true.
2. Both A and R are false.
3. A is false but R is true.
4. A is true but R is false.

Answer

A is false but R is true.

Explanation

Assertion (A) is false. The center of gravity of an irregularly-shaped object does not always coincide with its geometric center. It depends on the distribution of mass within the object.

Reason (R) is true. The center of gravity does depend on the distribution of mass within an object.

Assertion (A): A crack in a glass vessel often shines like a mirror.

Reason (R): It shines due to the refraction of light.

1. Both A and R are true.
2. Both A and R are false.
3. A is false but R is true.
4. A is true but R is false.

Answer

A is true but R is false.

Explanation

Assertion (A) is true. A crack in a glass vessel shines like a mirror because of the reflection of light from the cracked surfaces.

Reason (R) is false. The shine of the crack is not due to the refraction of light but due to the reflection of light.

Assertion (A): The focal length of a lens does not change when red light is replaced by blue light.

Reason (R): The focal length of a lens depends on the refractive index of material of lens.

1. Both A and R are true.
2. Both A and R are false.
3. A is false but R is true.
4. A is true but R is false.

Answer

A is false but R is true.

Explanation

Assertion (A) is false. The focal length of a lens does change when different colours of light are used. Different colours have different wavelength so focal length is different.

Reason (R) is true. The focal length (f) of a lens does depend on the refractive index of the material of the lens. It is inversely proportional to the refractive index of the medium μ.

Assertion (A): When a ray of light is refracted through a rectangular glass slab, there is no dispersion of light.

Reason (R): Dispersion of light is the phenomenon of splitting of white light into its constituent colours.

1. Both A and R are true.
2. Both A and R are false.
3. A is false but R is true.
4. A is true but R is false.

Answer

Both A and R are true.

Explanation

Assertion (A) is true. When a ray of light passes through a rectangular glass slab, there is no dispersion of light. After refraction at two parallel faces of a glass slab, the ray of light emerges in a direction parallel to the incident ray. As rays of all colours emerge in the same direction as incident ray, hence there is no dispersion, but only lateral displacement

Reason (R) is true. Dispersion of light is the phenomenon of splitting of white light into its constituent colors.

Assertion (A): A beam of white light gives a spectrum on passing through a hollow prism.

Reason (R): The speed of light outside the prism is same as the speed of light inside the prism.

1. Both A and R are true.
2. Both A and R are false.
3. A is false but R is true.
4. A is true but R is false.

Answer

Both A and R are false.

Explanation

Assertion (A) is false. A beam of white light does give a spectrum when passing through a prism, but it is not a "hollow" prism that causes this dispersion. A hollow prism contains air in it, so when a beam of white light is passed through it, it does not give a spectrum. Because light is passed to air through air, so no spectrum will be produced.

Reason (R) is false. The speed of light inside a medium, such as a glass prism, is generally slower than the speed of light in vacuum. So the speed of light outside the prism is greater than the speed of light inside the glass prism.

Assertion (A): If the angles of the base of a prism are equal, then in the position of minimum deviation, the refracted ray will pass parallely to the base of the prism.

Reason (R): For minimum deviation, angle of incidence is equal to the angle of emergence.

1. Both A and R are true.
2. Both A and R are false.
3. A is false but R is true.
4. A is true but R is false.

Answer

Both A and R are true.

Explanation

Assertion (A) is true. If the angles of the base of a prism are equal, then at minimum deviation condition for prism the angle of incidence is equal to the angle of emergence and the refracted ray inside the prism is parallel to the base of the prism

Reason (R) is true. For the minimum deviation to occur, the angle of incidence must be equal to the angle of emergence. This ensures that the deviation caused by the prism is minimized.

Assertion (A): The stars twinkle while the planets do not.

Reason (R): Stars are more distant than the planets.

1. Both A and R are true.
2. Both A and R are false.
3. A is false but R is true.
4. A is true but R is false.

Answer

Both A and R are true.

Explanation

Assertion (A) is true. Planets do not twinkle because, unlike stars, they are seen as extended sources of light. When observing a planet, which appears as a disk rather than a point of light, the combined effect of a large number of point-sized sources averages out the total variation in the amount of light entering the observer's eye. This averaging effect nullifies the twinkling phenomenon, making planets appear steady in brightness.

Reason (R) is true. Planets are much closer to us than stars, so they are not point-sized objects to our eye. Hence, the fluctuations have a negligible effect and they don't seem to twinkle.

Assertion (A): An empty test tube placed in water in a beaker with its mouth outside the water surface appears silvery when viewed from a suitable direction.

Reason (R): The substance in water appears silvery due to refraction of light.

1. Both A and R are true.
2. Both A and R are false.
3. A is false but R is true.
4. A is true but R is false.

Answer

A is true but R is false.

Explanation

Assertion (A) is true. An empty test tube placed in water in a beaker with its mouth outside the water surface appears silvery when viewed from a suitable direction because of the phenomenon of total internal reflection at the air-water interface, which can create a silvery appearance.

Reason (R) is false. Substance in water appears silvery due to the refraction of light, is incorrect. The silvery appearance typically arises due to total internal reflection, not refraction.

Assertion (A): Sound waves can travel in vacuum, but light waves cannot.

Reason (R): Light is a mechanical wave, but sound is an electromagnetic wave.

1. Both A and R are true.
2. Both A and R are false.
3. A is false but R is true.
4. A is true but R is false.

Answer

Both A and R are false.

Explanation

Assertion (A) is false. Sound waves require a medium to propagate, such as air, water, or solids, but they cannot travel through a vacuum. On the other hand, light waves can propagate through vacuum.

Reason (R) is false. Light is not a mechanical wave; it is an electromagnetic wave. Similarly, sound is not an electromagnetic wave; it is a mechanical wave.

Assertion (A): When a force retards the motion of a body, the work done by the body is zero.

Reason (R): Work done depends on the angle between force and displacement.

1. Both A and R are true.
2. Both A and R are false.
3. A is false but R is true.
4. A is true but R is false.

Answer

A is false but R is true.

Explanation

Assertion (A) is false. When the force retards the motion, the work done is negative not zero.

Reason (R) is true. Work done depends on the angle between force and displacement W = F x S cos θ and cos 180 is -1, hence, W = - F x S

Assertion (A): If momentum of a body increases by 50%, its kinetic energy will increase by 125%.

Reason (R): Kinetic energy is proportional to the square of velocity.

1. Both A and R are true.
2. Both A and R are false.
3. A is false but R is true.
4. A is true but R is false.

Answer

Both A and R are true.

Explanation

Assertion (A) is true. When the momentum of a body increases by 50%, its kinetic energy will increase by 125%.

Let initial momentum be p and kinetic energy be K

If p increases by 50%, the new momentum p' = p + $\dfrac{p}{2}$ = $\dfrac{3p}{2}$

Relation between kinetic energy and momentum is given by; K = $\dfrac{p^2}{2m}$

So, $\dfrac{K'}{K}$ = $\dfrac{\dfrac{p'^2}{2m}}{\dfrac{p^2}{2m}}$ = $\dfrac{p'^2}{p^2}$ = $\dfrac{\Big(\dfrac{3p}{2}\Big)^2}{\dfrac{p^2}{1}}$ = $\dfrac{9}{4}$

So,

Percentage increase in kinetic energy = $\dfrac{K'-K}{K}$ x 100

= $\dfrac{ \dfrac{9K}{4} -K}{K}$ x 100

= $\dfrac{ \dfrac{9K-4K}{4}}{K}$ x 100

= $\dfrac{ \dfrac{5K}{4}}{K}$ x 100

= $\dfrac{5}{4}$ x 100 = 125%

Hence, kinetic energy will increase by 125%.

Reason (R) is true. Kinetic energy is proportional to the square of velocity, according to the formula: KE = $\dfrac{1}{2}$mv².

Assertion (A): The speed of sound in a gas increases with an increase in humidity.

Reason (R): Density of a gas decreases with increase in humidity.

1. Both A and R are true.
2. Both A and R are false.
3. A is false but R is true.
4. A is true but R is false.

Answer

Both A and R are true.

Explanation

Assertion (A) is true. When the humidity of a gas increases, the speed of sound increases because the density of humid air is less than the density of dry air. As the density of the medium decreases, the speed of sound in the medium increases. Hence, the speed of sound is faster in humid air than the dry air.

Reason (R) is true. The density of a gas does decrease with an increase in humidity.

Assertion (A): The flash of lightening is seen before the sound of thunder is heard.

Reason (R): The speed of sound is greater than the speed of light.

1. Both A and R are true.
2. Both A and R are false.
3. A is false but R is true.
4. A is true but R is false.

Answer

A is true but R is false.

Explanation

Assertion (A) is true. The flash of lightning is seen before the sound of thunder is heard due to the difference in the speeds of light and sound. Light travels much faster than sound, so the flash of lightning is observed almost instantaneously, while the sound of thunder takes some time to travel to the observer.

Reason (R) is false. The speed of sound is not greater than the speed of light. Light travels faster than sound with a speed of 3 x 10⁸ m/s whereas speed of sound is 330 m/s.

Assertion (A): When we start filling an empty pitcher with water, the pitch of the sound produced goes on decreasing.

Reason (R): The pitch of sound increases with increase in frequency.

1. Both A and R are true.
2. Both A and R are false.
3. A is false but R is true.
4. A is true but R is false.

Answer

A is false but R is true.

Explanation

Assertion (A) is false. As the pitcher fills up, the air column or amount of air inside the bottle decreases. The frequency of the note produced = $\dfrac{v}{4L}$, where v is the velocity of sound in air and L is length of air column, which is equal to depth of water level from the open end. As the pitcher is filled with water, L decreases. Therefore, frequency of sound produced goes on increasing. With increasing frequency the pitch of the sound produced also increases.

Reason (R) is true. The pitch of sound increases with increase in frequency.

Assertion (A): A ray of light travelling from a rarer medium to a denser medium, slows down and bends away from the normal.

Reason (R): The speed of light is higher in a rarer medium than in a denser medium.

1. Both A and R are true.
2. Both A and R are false.
3. A is false but R is true.
4. A is true but R is false.

Answer

A is false but R is true.

Explanation

Assertion (A) is false. When a ray of light travels from a rarer medium to a denser medium, it slows down and bends towards the normal. This is due to the change in speed and direction of light when it crosses the boundary between two different mediums, which is known as refraction.

Reason (R) is true. The speed of light is higher in a rarer medium (e.g., air) compared to a denser medium (e.g., glass or water). This difference in speed is what causes the refraction of light when it passes from one medium to another.

Assertion (A): A current carrying solenoid when suspended freely sets itself in the north-south direction just like a bar magnet.

Reason (R): The end of the solenoid where the direction of current is anti-clockwise behaves as a north pole and the end where the direction of the current is clockwise behaves as a south pole.

1. Both A and R are true.
2. Both A and R are false.
3. A is false but R is true.
4. A is true but R is false.

Answer

Both A and R are true.

Explanation

Assertion (A) is true. A current-carrying solenoid behaves like a magnet and aligns itself in the north-south direction when freely suspended, similar to a bar magnet. This behavior is due to the magnetic field produced by the current flowing through the solenoid.

Reason (R) is true. The direction of the magnetic field inside a solenoid depends on the direction of the current. The end of the solenoid where the current circulates anti-clockwise acts as a north pole, while the end where the current circulates clockwise acts as a south pole.

Assertion (A): The strength of the magnetic field produced due to a current carrying circular coil increases with an increase in the strength of the current.

Reason (R): Magnetic field strength is inversely proportional to the current flowing in a coil.

1. Both A and R are true.
2. Both A and R are false.
3. A is false but R is true.
4. A is true but R is false.

Answer

A is true but R is false.

Explanation

Assertion (A) is true. The strength of the magnetic field produced due to a current carrying circular coil increases with an increase in the strength of the current. This is consistent with Ampere's law, which states that the magnetic field is directly proportional to the current flowing through the coil.

Reason (R) is false. The magnetic field strength is directly proportional to the current flowing through a coil, not inversely proportional.

Assertion (A): Out of α, β and γ radiation, α-particles have maximum penetrating power.

Reason (R): The α-particles are the heaviest amongst the three.

1. Both A and R are true.
2. Both A and R are false.
3. A is false but R is true.
4. A is true but R is false.

Answer

A is false but R is true.

Explanation

Assertion (A) is false. Out of α, β and γ radiation, γ-particles have maximum penetrating power.

Reason (R) is true. The penetrating power of a particle depends upon the energy carried by it, its mass and the charge carried by it. A particle with a greater energy can use it to force itself into another medium and thereby penetrate it. α-particles rapidly dissipates its energy as it moves through the medium and therefore its penetrating power is quite small.

Assertion (A): The terminal voltage of a cell is always less than its e.m.f.

Reason (R): More the current drawn from the cell, the less is the terminal voltage.

1. Both A and R are true.
2. Both A and R are false.
3. A is false but R is true.
4. A is true but R is false.

Answer

A is false but R is true.

Explanation

Assertion (A) is false. E.m.f. is greater than the terminal voltage only when the cell delivers the current to the external circuit.

Reason (R) is true. When a heavy current is drawn from the cell, a large number of charge carriers flow through the electrolyte and hence more work is done. This results in more voltage drop v, and hence less terminal voltage V. Thus, terminal voltage V of a cell depends on the amount of current I drawn from it.

Assertion (A): ¹⁴₆C and ¹⁴₇N are isobars.

Reason (R): ¹⁴₆C has 6 protons and 8 neutrons in its nucleus, whereas ¹⁴₇N has 7 protons and 7 neutrons in its nucleus.

1. Both A and R are true.
2. Both A and R are false.
3. A is false but R is true.
4. A is true but R is false.

Answer

Both A and R are true.

Explanation

Assertion (A) is true. Isobars have the same mass number but different atomic numbers. Both ¹⁴₆C (carbon-14) and ¹⁴₇N (nitrogen-14) have a mass number of 14, making them isobars.

Reason (R) is true. ¹⁴₆C has 6 protons and 8 neutrons, while ¹⁴₇N has 7 protons and 7 neutrons both have mass number equal to 14, hence are isobars.

Assertion (A): When a hammer is made to fall on a nail fixed upright on a wooden piece, the nail begins to penetrate the wood.

Reason (R): As the hammer starts falling, its kinetic energy begins to change into potential energy.

1. Both A and R are true.
2. Both A and R are false.
3. A is false but R is true.
4. A is true but R is false.

Answer

A is true but R is false.

Explanation

Assertion (A) is true. When a hammer is made to fall on a nail fixed upright on a wooden piece, the nail begins to penetrate the wood due to the force applied by the falling hammer.

Reason (R) is false. The statement about the conversion of kinetic energy into potential energy as the hammer falls is incorrect. Potential energy is the energy that is stored in an object due to its position above the earth's surface. Hence, when a hammer is lifted it stores potential energy in it and when the hammer starts falling, this potential energy begins to change into kinetic energy and is used in driving a nail into the wood.

Assertion (A): The mechanical advantage of class III levers is always less than 1.

Reason (R): This is because the effort arm is always greater than the load arm.

1. Both A and R are true.
2. Both A and R are false.
3. A is false but R is true.
4. A is true but R is false.

Answer

A is true but R is false.

Explanation

Assertion (A) is true. Class III levers always have a mechanical advantage less than 1, indicating that the load force is greater than the effort force.

Reason (R) is false. In class III levers, the load arm is always longer than the effort arm. Therefore, the statement that the effort arm is always greater than the load arm is incorrect.

Assertion (A): A fuse wire must have a high resistance and low melting point.

Reason (R): A fuse is only used for a small current flow.

1. Both A and R are true.
2. Both A and R are false.
3. A is false but R is true.
4. A is true but R is false.

Answer

A is true but R is false.

Explanation

Assertion (A) is true. A fuse wire must have a high resistance to generate enough heat when a high current flows through it, causing it to melt and break the circuit.

Reason (R) is false. While fuses are used for protecting electrical circuits, they are not specifically used only for small current flow. Fuses are designed to handle normal operating currents but melt and break the circuit when the current exceeds a safe level, regardless of whether it is small or large.

Assertion (A): The specific heat capacity of a substance is the amount of heat required to raise its temperature by 1°C.

Reason (R): The specific heat capacity of a substance is not its characteristic property.

1. Both A and R are true.
2. Both A and R are false.
3. A is false but R is true.
4. A is true but R is false.

Answer

Both A and R are false.

Explanation

Assertion (A) is false. The specific heat capacity of a substance is the amount of heat required to raise the temperature of one unit mass of the substance by 1°C (or 1 K).

Reason (R) is false. The specific heat capacity of a substance is its characteristic property. It represents the substance's ability to store heat energy per unit mass and is an intrinsic property that is unique to each substance.

Assertion (A): The principle of the method of mixtures involves mixing substances at different temperatures to find the final temperature.

Reason (R): The law of conservation of energy states that the energy is neither created nor destroyed in an isolated system.

1. Both A and R are true.
2. Both A and R are false.
3. A is false but R is true.
4. A is true but R is false.

Answer

Both A and R are true.

Explanation

Assertion (A) is true. The principle of the method of mixtures involves mixing substances at different temperatures to find the final temperature. This method is based on the principle that heat lost by the hotter substance is equal to the heat gained by the colder substance when they reach thermal equilibrium.

Reason (R) is true. The law of conservation of energy states that energy is neither created nor destroyed in an isolated system. This principle is fundamental in understanding heat transfer processes, including the method of mixtures. In the method of mixtures, the total energy of the system (the substances being mixed) remains constant, as energy is transferred from the hotter substance to the colder substance until thermal equilibrium is reached.

Assertion (A): A transformer can increase the voltage of an alternating e.m.f.

Reason (R): This is achieved by keeping the number of turns in the secondary coil less than the number of turns in the primary coil.

1. Both A and R are true.
2. Both A and R are false.
3. A is false but R is true.
4. A is true but R is false.

Answer

A is true but R is false.

Explanation

Assertion (A) is true. A transformer can increase the voltage of an alternating electromotive force (e.m.f.). This is accomplished through electromagnetic induction, where a changing magnetic field in the primary coil induces a voltage in the secondary coil.

Reason (R) is false. To increase the voltage in the secondary coil, the number of turns in the secondary coil must be greater than the number of turns in the primary coil, not less. This allows for a step-up transformation of voltage.

Assertion (A): A transformer cannot be used with a direct current.

Reason (R): The lamination of core prevents the loss of energy due to induced currents in the core.

1. Both A and R are true.
2. Both A and R are false.
3. A is false but R is true.
4. A is true but R is false.

Answer

Both A and R are true.

Explanation

Assertion (A) is true. A transformer cannot be used with direct current (DC) because it relies on the principle of electromagnetic induction, which requires a changing magnetic field. In DC, the current flows in one direction without changing, so there is no alternating magnetic field to induce voltage in the secondary coil of the transformer.

Reason (R) is true. The lamination of the core in a transformer is used to prevent energy loss due to induced currents in the core, known as eddy currents. By laminating the core, the magnetic flux is confined to the individual lamination, reducing the eddy current losses

Assertion (A): Same current flows through the live wires and the filament of a bulb, but the heat produced in the filament is much higher.

Reason (R): The filament of a bulb is made of low resistance and high melting point.

1. Both A and R are true.
2. Both A and R are false.
3. A is false but R is true.
4. A is true but R is false.

Answer

A is true but R is false.

Explanation

Assertion (A) is true. Same current flows through the live wires and the filament of a bulb, but the heat produced in the filament is much higher. This is due to the higher resistance of the filament compared to the live wires, leading to greater heat generation in the filament.

Reason (R) is false. The filament of a bulb is not made of a material with low resistance. In fact, the filament is specifically designed to have a relatively high resistance. This high resistance allows it to produce light efficiently by converting electrical energy into heat and then into light.

Assertion (A): The magnitude of induced e.m.f. becomes maximum when the magnetic flux linked with the coil reduces to zero from its maximum value.

Reason (R): This happens when the plane of the coil lies in the direction of the magnetic field.

1. Both A and R are true.
2. Both A and R are false.
3. A is false but R is true.
4. A is true but R is false.

Answer

Both A and R are true.

Explanation

Assertion (A) is true. According to Faraday's law of electromagnetic induction, the magnitude of the induced electromotive force (e.m.f.) in a coil is maximum when the rate of change of magnetic flux through the coil is maximum. This occurs when the magnetic flux linked with the coil reduces to zero from its maximum value, resulting in the maximum rate of change of magnetic flux.

Reason (R) is true. This happens when the plane of the coil lies in the direction of the magnetic field. When the coil is in this position, the magnetic flux through the coil is changing most rapidly, resulting in the maximum induced e.m.f.