Question

Assertion: If a man with a wrist watch on his hand falls from the top of a tower, its watch gives correct time during the free fall.
Reason: The working of the wrist watch depends on spring action and it has nothing to do with gravity.
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion.
B. Both Assertion and Reason are correct but Reason is not the correct explanation for assertion.
C. Assertion is correct but Reason is incorrect.
D. Assertion is incorrect but Reason is correct.

Answer 1

The hands of the wrists watch rotates as the spring releases potential energy stored in it. Recall the expression for the potential energy stored in the spring and check whether the potential energy depends on the acceleration due to gravity. The wrist watch is powered by a battery and hence it is a mechanical device.

Complete answer:
We know that the wrist watch works on the spring action. The potential energy stored in the spring is released and thus the hands of the watch rotate. We have the potential energy stored in the spring of force constant k is,
$U = \dfrac{1}{2}k{x^2}$, where, x is the displacement from the mean position.
We can see from the above formula, the potential energy stored in the spring is independent of the acceleration due to gravity. Even if the acceleration due to gravity changes, the wrist watch will give the correct time because the wrist watch is a mechanical device and it has nothing to do with the gravity.

So, the correct answer is option A.

Additional information:
The wrist watch will show reduced time only when we travel with the fraction of speed of light. This phenomenon is known as time dilation which is explained by Albert Einstein in the Special Theory of Relatively. The time runs slower in the accelerated frame of reference by the expression, $t' = \dfrac{t}{{\sqrt {1 - \dfrac{{{v^2}}}{{{c^2}}}} }}$, where, t is the original time, v is the velocity of the accelerated frame and c is the speed of light.

Note: The mechanical watches provide constant energy for the rotation of the mainspring. The potential energy stored in the spring never gets reduced until the supply from the battery ceases. Note that the gravity affects the motion of the pendulum since its time period depends on the acceleration due to gravity. But there is not such a pendulum in the wrist watches.