Question

A cuboidal car of height 3 m is slipping on a smooth inclined plane. A bolt released from the roof of car from the centre of roof (P) then distance from centre of roof where bolt hits the floor with respect to car is:

A) 5 m
B) 4 m
C) 3 m
D) None of these

Answer 1

Hint: In this case, the bolt and car both, are in motion. Hence, in order to understand the motion of the bolt, we have to consider the motion in relation to the car since the car is also, moving down the inclined plane.

Complete step by step solution:
Consider a cuboidal car placed at a height of 3m from the ground on an inclined plane.
P is the point where the bolt is present and from where, the bolt is released to the ground.
Here we see that there is a weight exerted by the bolt which leads to its acceleration.
Weight exerted by the bolt, $w = mg$
The component of acceleration of the bolt with respect to the car is –
$\Rightarrow \dfrac{{w\sin \theta }}{m} = g\sin \theta $
Weight exerted by the car, $W = Mg$
Acceleration of the car down the inclined plane is equal to –
$\Rightarrow \dfrac{{W\sin \theta }}{M} = g\sin \theta $
Thus, we see here that the values of acceleration of the bolt with respect to the car and the acceleration of the car down the inclined plane is equal to $g\sin \theta $.
So, if we take the frame of reference inside the car, the bolt appears to have no motion since both the bolt and the car have the same values of acceleration.
This means that the bolt falls to the ground at the same instant as that of the car.
Given that the car touches the ground after sliding down a height of 3m, it can be said that the bolt also takes the same distance of 3m to touch the ground.
Hence, the distance from the roof where the bolt hits the ground is equal to 3 m.

Hence, the correct option is Option C.

Note: The frame of reference concept which is explained in brief here, is the same reason that we fall as if the objects outside the car/train are moving backwards while riding inside the car/train since our relative motion with respect to the car/train is zero.