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Question

A car is moving in a circular horizontal track of radius 10 m with a constant speed of 10 m/s. A bob is suspended from the roof of the car by a light rigid rod. The angle (in degrees) made by the rod with the vertical is
[Take g=10 m/s2]

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Solution

Given,
Radius of track, r=10 m
Speed of car, u=10 m/s

Let us suppose tension in rod is T, making angle θ with the vertical and mass of bob is m.

From car frame of reference :-
As car is going around a circular horizontal track, it is in accelerated motion. Therefore, we have to apply pseudo force on bob of magnitude ma in the opposite direction of centripetal acceleration of the car.


Acceleration of car is a.
a=u2r [ Circular Motion ]
=10210
=10 m/s2 (inward).......(1)

F.B.D of bob :


On applying F=ma along horizontal.
Tsinθma=0
Tsinθ=ma .......(2)

On applying F=ma along vertical :
Tcosθmg=0
Tcosθ=mg ........(3)

On dividing equation (2) by (3) :.
tanθ=ag
tanθ=1010 [ from equation 1 ]
tanθ=1
θ=45

The angle made by the rod with the vertical is 45.

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