Question

A van accelerates uniformly down an inclined hill going from rest to 30 m/s in 6 s. During the acceleration, a toy of mass m = 0.1 kg hangs by a light string from the van's ceiling. The acceleration is such that string remains perpendicular to the ceiling. (Take g = 10 $m/s^2$).
choose the correct option(s)

• A. The angle $\theta$ of the incline is ${30}^0$
• B. The angle $\theta$ of the incline is ${60}^0$
• C. The tension in string is $\frac{\sqrt{3}}{2}$ N
• D. The tension in string is 1 N

Answer 1

The correct option is A The angle $\theta$ of the incline is ${30}^0$

$\begin{array}{c}Acceleration=\frac{30}{6}=5m/s^2\\ ma=mg\sin \theta \\ So,\theta =arc\sin \left(\frac{a}{g}\right)=arc\sin \left(\frac{5}{9.8}\right)={30.6}^0={30}^0\end{array}$

Hence,

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