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

Options

A. `theta=tan^(-1)((1)/(9))`
B. `theta=tan^(-1)((8)/(9))`
C. `theta=sin^(-1)((1)/(9))`
D. `theta=cos^(-1)((1)/(9))`

Answer

A

Explanation

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