Assertion (A): The internal area of cross-section of a pipe is 21 cm². Water runs through this pipe at a speed of 5 km/h. The volume of water that runs through the pipe in 2 minutes = 21 cm² x 5 km/h x 2 minutes

Reason (R): The volume of water that runs through the pipe in 2 minutes = area of cross-section in cm² x speed of water through it in cm/s x time in seconds

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

A is false, R is true.

Explanation

Given,

The internal area of the cross-section of the pipe = 21 cm²

Speed of water = 5 km/h = $\dfrac{5,00,000}{60}$ cm/min

Volume of water that flows in unit time = Area of cross-section x speed of flow of water

= 21 cm² x $\dfrac{5,00,000}{60}$ cm/min

Total time = 2 min

Total volume = Volume x Total time

= 21 cm² x $\dfrac{5,00,000}{60}$ cm/min x 2 min

But according to Assertion, the volume of water that runs through the pipe in 2 minutes = 21 cm² x 5 km/h x 2 minutes (≠ 21 cm² x $\dfrac{5,00,000}{60}$ cm/min x 2 min)

∴ Assertion (A) is false.

Volume of water that flows in unit time = Area of cross-section x speed of flow of water

∴ The volume of water that runs through the pipe in 2 minutes = area of cross-section in cm² x speed of water through it in cm/s x time in seconds

∴ Reason (R) is true.

Hence, Assertion (A) is false, Reason (R) is true.