Question

Consider the following data and choose the correct option.

$1.$ The time period of a simple pendulum, whose bob is a hollow metallic sphere is $T$.
$2.$ The time period of a simple pendulum is $T_1,$ when the bob is filled with sand,
$3.$ The time period of a simple pendulum is $T_2,$ when it is filled with mercury and
$4.$ The time period of a simple pendulum is $T_3,$ when it is half-filled with mercury as shown.

• 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

The correct option is D $T=T_1=T_2<T_3$

Time period of a pendulum doesnot depend upon mass, but it depends upon length (distance between point of suspension and centre of mass)
In first $3$ cases, distance between point of suspension and centre of mass are same.
So, $T=T_1=T_2,$
In last case, when mercury is filled half of the bob, the distance between point of suspension and centre of mass is more than in previous cases.
So, $T_3$ will be more than in other cases.
Hence 'D' is the correct option.