Question

A man having a wrist watch and a pendulum clock rises on a TV tower. The wrist watch and pendulum clock perchance fall from the top of the tower. Then
 

A. Both will keep correct time during the fall.
B. Both will keep incorrect time during the fall.
C. Wrist watch will keep correct time and clock will become fast.
D. Clock will stop but wrist watch will function normally.

Answer 1

Hint:The above problem can be resolved using a simple pendulum and the mathematical relation for the oscillation time period. The simple logic being used to resolve this problem is that, when the pendulum clock is dropped from a certain height, then the acceleration due to gravity will become zero at a specific point of the ground. And this will cause the magnitude of gravitational acceleration to be zero. And according to the formula of the time period, when this value is substituted, the clock's time will be shown as infinity. And this concludes the non-functioning of the clock.

Complete step by step answer:
We know the expression for the time period T of the pendulum clock is,
\[T = 2\pi \sqrt {\dfrac{l}{g}} \]
From the above expression, it is clear that the functioning of the watch depends on the action of spring. Hence it can be concluded that the functioning of the watch will not be affected by the gravity. Moreover, when there is the free fall of the watch, then the magnitude of acceleration will become zero and the time period will become infinity as,
 \[\begin{array}{l}
T = 2\pi \sqrt {\dfrac{l}{g}} \\
T = 2\pi \sqrt {\dfrac{l}{0}} \\
T = \infty
\end{array}\]
Hence, the clock will stop.
Therefore, the clock will stop but the wrist watch will function normally.

Note: Try to remember the mathematical formula for the time period of the simple pendulum. Then apply the concepts and the applications of this formula in many cases like, one such case is that when the clock is being dropped, then the effect on the time period is to be analysed.