Q. A simple pendulum of length $l$ 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 2 T. then new length is
A) $2\ l$
B) $4\ l$
C) $4\ lx$
D) $4\ l/x$
Explanation
(b) $T = 2\pi\sqrt{\frac{l}{g}}$
and $2T = 2\pi\sqrt{\frac{l}{g}}$
Then $\frac{1}{2} = \sqrt{\frac{l}{l^{'}}}\ \ or\ \ l^{'}\text{=}4l$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.