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A ball is suspended on a thread from the...

A ball is suspended on a thread from the ceiling of a car. The breakes are applied and the speed of car changes from `5m//sec` to `5//3m//sec` during the time interval of 3 seconds. Find the angle that the thread with the ball will deviate from vertical.

A

`theta=tan^-1((1)/(9))`

B

`theta=tan^-1((8)/(9))`

C

`theta=cos^-1((1)/(9))`

D

`theta=sin^-1((1)/(9))`

Text Solution

Verified by Experts

The correct Answer is:
A

The situation is shown in figure. When the car moves towards right with acceleration a the rope carrying the mass makes an angle `theta`. Forces acting on the body are:
(1) Weight mg downwards.
(2) Tension T in the rope.
(3) Pseudo force ma towards left.
Since the body is in equilibrium under the action of three forces, we van apply condition of equilibrium.
`Tcostheta-mg=0`,`Tsintheta=ma`
`tantheta=(a)/(g)` or `a=gtantheta`
`tantheta=(a)/(g)` or `a=gtantheta`
Acceleration, `a=(1)/(3)(5-(5)/(3))=(10)/(9)(m)/(sec^2)`
`(10)/(9)=10tantheta` or `tantheta=(1)/(9)impliesthetatan^-1((1)/(9))`
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