A simple pendulum is set up on a trolley which slides down a frictionless inclined plane making an angle θ with horizontal. The time period of pendulum is

Question

A simple pendulum is set up on a trolley which slides down a frictionless inclined plane making an angle θ with horizontal. The time period of pendulum is (A) 2 π √(l/g) (B) 2 π √(l cos θ/g) (C) 2 π √(l/g cos θ) (D) 2 π √(l/g(1- cos θ))

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/efb73101fc3635424a28d1f3c5b4d463-.png" /> At equilibrium, inside the trolley, Tension =m g cos θ Hence effective g'=g cos θ T=2 π √(l/g')=2 π √(l/g cos θ)

Q. A simple pendulum is set up on a trolley which slides down a frictionless inclined plane making an angle $θ$ with horizontal. The time period of pendulum is

$2 π \frac{l}{g}$

$2 π \frac{l c o s θ}{g}$

$2 π \frac{l}{g c o s θ}$

$2 π \frac{l}{g ( 1 - c o s θ )}$

At equilibrium, inside the trolley, Tension $= m g cos θ$ Hence effective $g^{'} = g cos θ$
$T = 2 π \frac{l}{g ^{'}} = 2 π \frac{l}{g c o s θ}$

Q. A simple pendulum is set up on a trolley which slides down a frictionless inclined plane making an angle θ with horizontal. The time period of pendulum is

2πgl​​

2πglcosθ​​

2πgcosθl​​

2πg(1−cosθ)l​​