Question

A trolley is accelerating down an incline of angle $\theta$ with acceleration $gsin\theta$. Which of the following is correct? ($\alpha$ is the constant angle made by the string with vertical).

• A. $\alpha =\theta$
• B. $\alpha =0^{\circ }$
• C. Tension in the string, T = mg
• D. Tension in the string, T = mg sec $\theta$

Answer 1

The correct option is A $\alpha =\theta$

From figure, tension in the string is $T=mgcos\alpha -\left(1\right)$

As the trolley is falling freely in the direction of inclined plane, the tension only balances that component of gravitational force which is normal to the inclined plane.

$T=mgcos\theta -\left(2\right)$

from $\left(1\right)$ and $\left(2\right)$,

$cos\alpha =cos\theta ⟹\alpha =\theta$