Question

A trolley is falling freely on inclined plane as shown in the figure. The angle of string of pendulum with the ceiling of trolley is $\left(\alpha \right)$ equal to

• A. ${\theta }^{\circ }$
• B. ${90}^{\circ }-{\theta }^{\circ }$
• C. ${90}^{\circ }$
• D. $0^{\circ }$

Answer 1

The correct option is C ${90}^{\circ }$

Component of tension force along the plane $=Tcos\alpha$

Component of weight along the plane $=mgsin\theta$

Acceleration of the car $=$ Acceleration of the bob in the car as the bob is in equilibrium in frame of the car

So, net force along the plane

$mgsin\theta +Tcos\alpha =ma$

$mgsin\theta +Tcos\alpha =m\left(gsin\theta \right)$

$Tcos\alpha =0$

But $T$ is not equal to zero so,

$cos\alpha =0$

Then,

$\alpha ={90}^0$