Question

A ball is suspended on a thread from the ceiling of a car. The brakes 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. $\theta =ta{n}^{-1}\left(\frac{1}{9}\right)$
• B. $\theta =ta{n}^{-1}\left(\frac{8}{9}\right)$
• C. $\theta =si{n}^{-1}\left(\frac{1}{9}\right)$
• D. $\theta =co{s}^{-1}\left(\frac{1}{9}\right)$

Answer 1

Answer: (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 can apply condition of equilibrium

$Tcos\theta -mg=0;Tsin\theta =ma$

$tan\theta =\frac{a}{g}$ or $a=gtan\theta$

Acceleration, $a=\frac{1}{3}\left(5-\frac{5}{3}\right)$

$=\frac{10}{9}m/se{c}^2$

$\frac{10}{9}=10tan\theta$ or

$tan\theta =\frac{1}{9}$

$\Rightarrow \theta =ta{n}^{-1}(\frac{1}{9})$