Question

A trolley is sliding on the smooth fixed wedge of inclination ${60}^o$ with horizontal. A pendulum is connected with the ceiling of trolley whose thread makes angle $\theta$ with vertical, then $\theta$ is equal to

• A. ${60}^o$
• B. ${30}^o$
• C. ${45}^o$
• D. $\varphi$

Answer 1

The correct option is D $\varphi$

As trolley is moving freely from rest. Its acceleration is $gsin\varnothing$ along the incline surface and the string is experiencing misleading force in an opposite direction$.$

Let us assume that pendulum is making an angle $\varnothing$ in vertical direction $:$

$Tcos\theta +mgsin\varnothing .sin\varnothing =mg$

$Tcos\theta =mg-mgsin²\varnothing$

$Tcos\theta =mgco{s}^2\varnothing$------------$\left(1\right)$

$Tsin\theta =mgsin\varnothing cos\varnothing$------------ $\left(2\right)$

comparing both the equations we get$,$

$\theta =\varnothing$

Hence,

option $\left(D\right)$ is correct answer.