Courses
Courses for Kids
Free study material
Offline Centres
More
Store

# A ball is suspended by a thread from the ceiling of a car. The brakes are applied and the speed of the car changes uniformly from $\mathop {36kmh}\nolimits^{ - 1}$ to zero in $5s$ . The angle by which the ball deviates from the vertical ($g = 10m{s^{ - 2}}$) is:(A) $ta{n^{ - 1}}(\frac{1}{3})$(B) $si{n^{ - 1}}(\frac{1}{5})$(C) $ta{n^{ - 1}}(\frac{1}{5})$(D) $co{t^{ - 1}}(\frac{1}{3})$

Last updated date: 14th Sep 2024
Total views: 79.5k
Views today: 0.79k
Verified
79.5k+ views
Hint We will first find out the acceleration of the car. Finally we will find out the angle it makes with the vertical.
Formulae Used: $a = \frac{{(v - u)}}{t}$
Where, $a$ is the acceleration of the body, $v$ is the final velocity, $u$ is the initial velocity and $t$ is the time taken by the body.

Complete Step By Step Solution
Here,
$u = {\text{ }}36{\text{ }}km{h^{ - 1}} = 10m{s^{ - 1}}$
$v = 0km{h^{ - 1}} = 0m{s^{ - 1}}$
$t = 5s$
Now,
${a_{car}} = \frac{{(0 - 10)}}{5}$
Now,
${a_{}} = - 2m{s^{ - 2}}$
$\begin{gathered} tan\theta = \frac{a}{g} = \frac{2}{{10}} = \frac{1}{5} \\ \\ \end{gathered}$
Thus, the answer turns out to be $\theta = ta{n^{ - 1}}(\frac{1}{5})$ which is (C).
But,
Also,
If we take
$\begin{gathered} sin\theta = \frac{2}{{10}} = \frac{1}{5} \\ \\ \end{gathered}$
$\Rightarrow \theta = si{n^{ - 1}}(\frac{1}{5})$

Hence, (B) is also correct.

Note We got the value of $sin\theta$ , we took ${a_{net}} = \sqrt {{a^2} + {g^2}}$ an d value turns out to be $10m{s^{ - 2}}$. Also, we took only the magnitude as it only plays the role to form the angle.