Question

The period of a simple pendulum, whose bob is a hollow metallic sphere, is $T .$ The 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? Hollow Sand Mercury

• A. $T = T_{1} = T_{2} > T_{3}$
• B. $T_{1} = T_{1} = T_{3} > T$
• C. $T > T_{3} > T_{1} = T_{2}$
• D. $T = T_{1} = T_{2} < T_{3}$

Answer 1

Answer: (D)

Time period of pendulum doesn't depends upon mass but it depends upon length (distance between point of suspension and centre of mass). In first three cases length are same so $T=T_{1}=T_{2}$ but in last case centre of mass lowers which in turn increases the length. So in this case time period will be more than the other cases.