A pendulum is suspended in a lift and its period of oscillation when the lift is stationary is T0. What must be the acceleration of the lift for the period of oscillation of the pendulum to be (T0/2)?

Question

A pendulum is suspended in a lift and its period of oscillation when the lift is stationary is T0. What must be the acceleration of the lift for the period of oscillation of the pendulum to be (T0/2)? (A) 2g downward (B) 2g upward (C) 3g downward (D) 3g upward

Tardigrade Admin · Accepted Answer

T0=2π √(ℓ /g) (T0/2)=2π √(ℓ /g + a) (√(ℓ /g)/2)=2π √(ℓ /g + a) (1/4 g)=(1/ g + a) g+a=4g a=3g upward

Q. A pendulum is suspended in a lift and its period of oscillation when the lift is stationary is $T_{0} .$ What must be the acceleration of the lift for the period of oscillation of the pendulum to be $\frac{T _{0}}{2} ?$

$2 g$ downward

$2 g$ upward

$3 g$ downward

$3 g$ upward

$T_{0} = 2 π \frac{ℓ}{g}$
$\frac{T _{0}}{2} = 2 π \frac{ℓ}{g + a}$
$\frac{\frac{ℓ}{g}}{2} = 2 π \frac{ℓ}{g + a}$
$\frac{1}{4 g} = \frac{1}{g + a}$
$g + a = 4 g$
$a = 3 g$ upward

Q. A pendulum is suspended in a lift and its period of oscillation when the lift is stationary is T0​. What must be the acceleration of the lift for the period of oscillation of the pendulum to be 2T0​​?

2g downward

2g upward

3g downward

3g upward