Question

A trolley car slides down a smooth inclined plane of angle of inclination $\theta $. If a body is suspended from the roof of the trolley car by an inextensible string of length l, the corresponding tension in the string will be
A. $mg$
B. $mg\cos \theta $
C. $mg\sin \theta $
D. None of these

Answer 1

Hint: One should first read the question properly and thus note down all the given quantities from the question. Now, you could go for making the free body diagram of the body that is being hung from the roof of the trolley. Then accordingly one could solve the question.

Complete step-by-step solution:
In the question we are given a trolley that slides down an inclined plane of inclination \[\theta \]and there is a body that is suspended from the roof of it by a string. We are supposed to find the tension that is present in the string. Let us first make a free body diagram of the body that is hung from the given conditions.

Let the body that is hung from the roof of the trolley be of m mass. Then we have a tension in the string along the string and then we have the weight of the body that is acting vertically downwards.
In addition to this we have pseudo force on the body up the plane. We have resolved the vector indicating the weight of the body into its respective components. Now on balancing the forces perpendicular to the incline plane to get,
$T=mg\cos \theta $
Therefore, we found the tension in the string to be $T=mg\cos \theta $.

Note: One should always be careful while making a free body diagram of a system. One should make sure that no force acting on the system is missed out. Accordingly one should make use of the pseudo force concept. Also, resolving of vectors should be done accordingly.