Question

A simple pendulum of length has a brass bob attached at its lower end. Its period is $T$. If a steel bob of same size, having density $ x $ times that of brass, replaces the brass bob and its length is changed, so that period becomes, $2T$ then new length is

• A. $ 2l $
• B. $ 4l $
• C. $ 4lx $
• D. $ \frac{41}{x} $

Answer 1

Answer: (B)

Time period of simple pendulum
$T=2 \pi \sqrt{\frac{l}{g}}$
Time period does not depend on density of bob.
$T \propto \sqrt{l}(l=$ length of pendulum)
$\frac{T_{1}}{T_{2}}=\sqrt{\frac{l_{1}}{l_{2}}}$
$\frac{T}{2 T}=\sqrt{\frac{l}{l_{2}}}$
Hence, $l_{2}=4 l$
Hence, new length is $4 l$.