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Q.

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. The angle that the thread will deviate from vertical.

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a

$θ = \tan^{- 1} (1 / 9)$

b

$θ = \sin^{- 1} (1 / 9)$

c

$θ = \cos^{- 1} (1 / 9)$

d

$θ = \tan^{- 1} (8 / 9)$

answer is A.

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Detailed Solution

The situation is shown in figure.
Question Image
When the car moves towards right with acceleration a the rope carrying the mass makes an angle .
Acceleration,
$\begin{aligned} a = \frac{1}{3} (5 - \frac{5}{3}) = \frac{10}{9} m / s^{2} \\ \Rightarrow & \tan θ = \frac{ma}{mg} = \frac{a}{g} \Rightarrow \frac{10}{9 \times 10} = \frac{1}{9} \end{aligned}$

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