Question

A person standing in a stationary lift measures the periodic time of a simple pendulum inside the lift to be equal to T. Now, if the lift moves along the vertically upward direction with an acceleration of (g/3), then the periodic time of the lift will now be……………

(A) √3T 

(B) √(3/2)T 

(C) (T/3) 

(D) (T/√3)

Answer 1

The correct option (B) √(3/2)T   

Explanation:

T = 2π √(ℓ/g) 

in stationary lift, time periods is T. When lift moves up with acceleration (g/3), effective acceleration is 

g' = g + (g/3) = (4/3)g

∴ New time period = T' = 2π √(ℓ/g') = 2π√{ℓ/(4/3)g} = √{(3/4)(ℓ/g)} × 2π 

T' = √(3/2) × 2π√(ℓ/g) 

T' = √(3/2)T