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Physics

Assertion (A) : If the distance between bodies of masses M1 and M2 is increased by a factor of 4, the gravitational force reduces by 1/16.

Reason (R) : The gravitational force is inversely proportional to the square of distance between two bodies.

  1. both A and R are true and R is the correct explanation of A
  2. both A and R are true and R is not the correct explanation of A
  3. assertion is false but reason is true
  4. assertion is true but reason is false

Motion in One Dimension

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Answer

both A and R are true and R is the correct explanation of A

Explanation

Assertion (A) is true because according to Newton’s law of gravitation :

F=GM1M2r2\text F=\text G\dfrac{\text M1\text M2}{\text r^2}

If distance r becomes 4 times, then :

F′=F42=F16\text F'=\dfrac {\text F}{4^2}=\dfrac {\text F}{16}

So, the force becomes 1/16th of the original.

​Reason (R) is true because this is exactly what Newton’s law states :

F∝1r2\text F\propto\dfrac{1}{\text r^2}

Since the reason correctly explains the assertion, both are true and reason is the correct explanation.

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