A car is moving in a circular horizontal track of radius 10m with a constant speed of 10m/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=10m/s2]
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Solution
Given,
Radius of track, r=10m
Speed of car, u=10m/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 =10m/s2 (inward).......(1)
F.B.D of bob :
On applying ∑F=ma along horizontal. Tsinθ−ma=0 ⇒Tsinθ=ma .......(2)
On applying ∑F=ma along vertical : Tcosθ−mg=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∘.