Question

The time period of a simple pendulum, whose bob is a hollow metallic sphere is T. Time period is $T_1$ when the bob is filled with sand, $T_2$ when it is filled with mercury, and $T_3$ when it is half-filled with mercury. Which of the following is true?

• A. $T=T_1=T_2>T_3$
• B. $T_1=T_2=T_3>T^{}$
• C. $T>T_3>T_1=T_2$
• D. $T=T_1=T_2<T_3$

Answer 1

The correct option is D

1. The time period of a pendulum doesn't depend upon mass, but it depends upon length (distance between the point of suspension and the center of mass of the bob).
2. Time period is given as $T=2\pi \sqrt{\frac{L}{g}}$
3. In the first three cases, lengths are the same. So T=$T_1$=$T_2$ but in the last case center of mass lowers which in turn increases the length. So in this case time period, $T_3$ will be more than the other cases.