JEE Main · 2022 · 29 Jul 2022 · Shift 1 · Elasticity & SHM

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The time period of oscillation of a simple pendulum of length L suspended from the roof of a vehicle, which moves without friction down an inclined plane of inclination

α

, is given by :

(A) $2 π L / (g cos α)$ ✓ Correct
(B) $2 π L / (g sin α)$
(C) $2 π L / g$
(D) $2 π L / (g tan α)$

Answer: (A)

Solution

When the vehicle moves down an inclined plane without friction, it accelerates with

a = g sin α

. In the non-inertial frame of the vehicle, a pseudo force acts on the pendulum. The effective gravity in this frame is

g_{eff} = g cos α

(perpendicular to the incline). The time period of the simple pendulum is

T = 2 π \frac{L}{g _{eff}} = 2 π \frac{L}{g c o s α}

JEE Main · 2022 · 29 Jul 2022 · Shift 1 · Single correct option

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