Calculate the time period of a simple pendulum of length L suspended from the roof of a vehicle which moves without friction down an inclined plane of inclination angle α .

Question

Calculate the time period of a simple pendulum of length L suspended from the roof of a vehicle which moves without friction down an inclined plane of inclination angle α . (A) 2π √(L/g c o s α ) (B) 2π √(L/g s i n α ) (C) 2π √(L/g) (D) 2π √(L/g t a n α )

Tardigrade Admin · Accepted Answer

See the following force diagram. <img class="img-fluid question-image" alt="Solution" src="https://cdn.tardigrade.in/q/nta/p-1ld3jammtsuj7cfz.jpg" /> Vehicle is moving down the frictionless inclined surface so, its acceleration is gsinα . Since vehicle is accelerating, a pseudo force m(g s i n α ) will act on bob of pendulum which cancel the sinα component of weight of the bob. Hence net force on the bob is Fn e t=mg cosα or net acceleration of the bob is ge f f=gcosα ∴ Time period T=2π √(l/ge f f)=2π √(1/g c o s α )

Q. Calculate the time period of a simple pendulum of length $L$ suspended from the roof of a vehicle which moves without friction down an inclined plane of inclination angle $α$ .

$2 π \frac{L}{g cos α}$

$2 π \frac{L}{g s in α}$

$2 π \frac{L}{g}$

$2 π \frac{L}{g t an α}$

Q. Calculate the time period of a simple pendulum of length L suspended from the roof of a vehicle which moves without friction down an inclined plane of inclination angle α .

2πgcosαL​​

2πgsinαL​​

2πgL​​

2πgtanαL​​

Q. Calculate the time period of a simple pendulum of length $L$ suspended from the roof of a vehicle which moves without friction down an inclined plane of inclination angle $α$ .

$2 π \frac{L}{g cos α}$

$2 π \frac{L}{g s in α}$

$2 π \frac{L}{g}$

$2 π \frac{L}{g t an α}$