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

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)  (41/x)

Tardigrade Admin · Accepted Answer

Time period of simple pendulum T=2 π √(l/g) Time period does not depend on density of bob. T propto √l(l= length of pendulum) (T1/T2)=√(l1/l2) (T/2 T)=√(l/l2) Hence, l2=4 l Hence, new length is 4 l.

Q. 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, $2 T$ then new length is

$2 l$

$4 l$

$4 l x$

$\frac{41}{x}$

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

Q. 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

2l

4l

4lx

x41​