Question

A car is moving in a circular horizontal track of radius 10m, with a constant speed of 10 m/s. A plump bob is suspended from the roof of the car by a light rigid rod. The angle made by the string with the vertical is?
A. ${{0}^{0}}$
B. ${{30}^{0}}$
C. ${{45}^{0}}$
D. ${{60}^{0}}$

Answer 1

Since, the car is moving in a circular motion, it is clear that the bob will not remain at rest and since it is hung from the vertical, it will get deflected and it will make some angle with the vertical. We need to find out all the forces acting on the bob. Since, it is hung from the top with the help of a string, tension will come into play.

Complete step by step answer:
Let the angle made by the bob with the vertical be $p$. Let us draw a diagram representing all the forces acting on the bob.

Whenever the body moves in a circular motion, the force which acts towards the centre is centripetal force given by $\dfrac{m{{v}^{2}}}{r}$. From the diagram above we see the forces acting.
$T\sin p=\dfrac{m{{v}^{2}}}{r}$ and $T\cos p=mg$
Upon dividing these two equations we get,
$\tan p=\dfrac{{{v}^{2}}}{rg}$
Let us put the values of velocity, radius and acceleration due to gravity we get,
$\tan p=\dfrac{100}{10\times 10}$
$\therefore \tan p=1$
We know the value of tan comes out to be 1 when the angle is ${{45}^{0}}$.

So, the correct option is C.

Note: Tension comes into the string and this tension always balances the centripetal force but since the body is in a circular motion, we have to resolve the forces into their components. when the body moves in a circular motion it has both linear velocity and angular velocity. If a particle moves with a constant speed then its speed remains constant but its velocity changes because velocity has both magnitude and direction.