A simple pendulum of length 1 m is freely suspended from the ceiling of an elevator. The time period of small oscillations as the elevator moves up with an acceleration of 2m/ s2 is (use g = 10m/ s2 )

Question

A simple pendulum of length 1 m is freely suspended from the ceiling of an elevator. The time period of small oscillations as the elevator moves up with an acceleration of 2m/ s2 is (use g = 10m/ s2 ) (A) (π/√5) s  (B) √(2/5) π s  (C) (π/√2) s  (D) (π/√3) s

Tardigrade Admin · Accepted Answer

Given, Length of simple pendulum (L)=1 m Acceleration (a)=2 m / s 2 Gravitation acceleration (g)=10 m / s 2 We know that, T=2 π √(1/g+a)=2 π √(1/10+2) =2 π √(1/12)=π √(4/12) I=(π/√3) s

Q. A simple pendulum of length $1 m$ is freely suspended from the ceiling of an elevator. The time period of small oscillations as the elevator moves up with an acceleration of $2 m / s^{2}$ is (use $g = 10 m / s^{2}$ )

$\frac{π}{5} s$

$\frac{2}{5} π s$

$\frac{π}{2} s$

$\frac{π}{3} s$

Given,
Length of simple pendulum $(L) = 1 m$
Acceleration $(a) = 2 m / s^{2}$
Gravitation acceleration $(g) = 10 m / s^{2}$
We know that,
$T = 2 π \frac{1}{g + a} = 2 π \frac{1}{10 + 2}$
$= 2 π \frac{1}{12} = π \frac{4}{12}$
$I = \frac{π}{3} s$

Q. A simple pendulum of length 1m is freely suspended from the ceiling of an elevator. The time period of small oscillations as the elevator moves up with an acceleration of 2m/s2 is (use g=10m/s2 )

5​π​s

52​​πs

2​π​s

3​π​s