The period of oscillation of simple pendulum of length l suspended from the roof of the vehicle which moves without friction, down an inclined plane of inclination α, is given by

Question

The period of oscillation of simple pendulum of length l suspended from the roof of the vehicle which moves without friction, down an inclined plane of inclination α, is given by (A) 2π√(L/g cos α) (B) 2π√(L/g sinα) (C) 2π√(L/g) (D) 2π√(L/g tanα)

Tardigrade Admin · Accepted Answer

We are given that the simple pendulum of length

l

is hanging from the roof of a vehicle which is moving down the frictionless inclined plane.
So, it's acceleration is

g s in θ

. since vehicle is accelerating a pseudo force m(g sin

θ

) will act on bob of pendulum which cancel the sin

θ

component of weight of the bob.
Hence we can say that the effective acceleration would be
equal to

g_{e ff} = g cos α

Now the time period of oscillation is given by

T = 2 π \frac{l}{g _{e ff}} = 2 π \frac{l}{g cos a}

Q. The period of oscillation of simple pendulum of length $l$ suspended from the roof of the vehicle which moves without friction, down an inclined plane of inclination $α$ , is given by

$2 π \frac{L}{g cos α}$

$2 π \frac{L}{g s in α}$

$2 π \frac{L}{g}$

$2 π \frac{L}{g t an α}$

Q. The period of oscillation of simple pendulum of length l suspended from the roof of the vehicle which moves without friction, down an inclined plane of inclination α, is given by

2πgcosαL​​

2πgsinαL​​

2πgL​​

2πgtanαL​​

Q. The period of oscillation of simple pendulum of length $l$ suspended from the roof of the vehicle which moves without friction, down an inclined plane of inclination $α$ , is given by

$2 π \frac{L}{g cos α}$

$2 π \frac{L}{g s in α}$

$2 π \frac{L}{g}$

$2 π \frac{L}{g t an α}$