As shown in the above figure, four simple pendulums with different bob are taken. Now, compare the time periods of these pendulums:

Question

As shown in the above figure, four simple pendulums with different bob are taken. Now, compare the time periods of these pendulums: (A) T=T1=T2>T3 (B) T1=T2=T3>T (C) T>T3>T1=T2 (D) T=T1=T2 < T3

Tardigrade Admin · Accepted Answer

We know that, Time period, T=2π √(l/g) where, l is the length of the pendulum. As we can see, the time period of the pendulum doesn't depend upon mass, but it depends upon length (distance between point of suspension and centre of mass of the bob).

Q.
As shown in the above figure, four simple pendulums with different bob are taken. Now, compare the time periods of these pendulums:

$T = T_{1} = T_{2} > T_{3}$

$T_{1} = T_{2} = T_{3} > T$

$T > T_{3} > T_{1} = T_{2}$

$T = T_{1} = T_{2} < T_{3}$

We know that,
Time period, $T = 2 π \frac{l}{g}$
where, $l$ is the length of the pendulum.
As we can see, the time period of the pendulum doesn't depend upon mass, but it depends upon length (distance between point of suspension and centre of mass of the bob).

Q. As shown in the above figure, four simple pendulums with different bob are taken. Now, compare the time periods of these pendulums:

T=T1​=T2​>T3​

T1​=T2​=T3​>T

T>T3​>T1​=T2​

T=T1​=T2​<T3​