Question

A second’s pendulum has time period 2 sec. The spherical bob which is empty has a mass of 50 gm. This is replaced by another solid bob of the same radius but having the mass of 100 gm. The new time period will be:
A. 4s
B. 1s
C. 2s
D. 8s

Answer 1

Hint: The time will be the same itself as the time period of the second’s pendulum is independent of mass of the bob used. Use the relation of the time period of the pendulum to find which factors are depending it answer.

Complete step-by-step answer:
As we all know, time period of the pendulum is given by,
${{T}_{new}}=2s$ $T=2\pi \sqrt{\dfrac{L}{g}}$
Where T is the time period in seconds, L is the length of the string and g is the acceleration due to gravity.
As we examine this equation, we can see that time period depends on the acceleration due to gravity. And apart from this, the time period of the bob depends on the length of the string used. The time period is independent of the mass of the bob. As per the question, the time period of the second's pendulum is 2 sec. And also the mass of the bob is the only thing which is changing. Therefore the time period remains the same.
 ${{T}_{new}}=2s$
Hence the correct answer is option C.

Note: The equation of time period of the pendulum should be noted well. Second’s pendulum is the pendulum having a time period of 2 seconds. A second’s pendulum is a special kind of pendulum which is having a time period precisely two seconds. One second is the time taken to oscillate in one direction and the other one second is the time taken in the opposite direction. So the correct answer is option C.