Question

In a legend the hero kicked a baby pig so that he is projected with a speed greater than that of his cry. If the wait of the baby pig is assumed to be $5kg$ and the time of contact $0.01\sec$ , the force with which the hero kicked him was:
$\begin{aligned} & (a)5\times {{10}^{-2}}N \\\ & (b)2\times {{10}^{5}}N \\\ & (c)1.65\times {{10}^{5}}N \\\ & (d)16.5\times {{10}^{3}}N \\\ \end{aligned}$

Answer 1

Since, it is mentioned in the question that the speed of baby is greater than the speed of cry, therefore the final speed of the baby pig must be greater than the speed of sound, i.e., $330m/\operatorname{s}$. Only under this condition will the baby pig be unable to hear his own cry, after being kicked by the hero.

Complete answer:
Let the initial speed of the baby pig be $u$.
Given, $u=0m/s$ [equation number $(1)$ ]
Also, let the final speed be $v$ . [equation number $(2)$]
Then, $v$ will be equal to the speed of sound, as it’s mentioned in the problem that the baby pig cannot listen to his own cry. Therefore,
$\Rightarrow v=330m/s$
And time $(t)$ is given as: $0.01s$ [equation number $(3)$]
We know, for a body undergoing straight line motion with constant acceleration:
$\Rightarrow v=u+at$
Putting the values of final speed$(v)$, initial speed$(u)$ and time taken$(t)$ from equations (1), (2) and (3), we get:
$\begin{aligned} & \Rightarrow 330=0+a(0.01) \\\ & \Rightarrow a=\dfrac{330}{0.01}m/{{s}^{2}} \\\ & \Rightarrow a=33000m/{{s}^{2}} \\\ & \\\ \end{aligned}$
Now, the force applied (say F) by the hero on the baby pig can be given by:
$\Rightarrow F={{M}_{pig}}(a)$
Where, ${{M}_{pig}}$ is the mass of the baby pig and its value is:
$\Rightarrow {{M}_{pig}}=5kg$
From the above equation, we have:
$\Rightarrow a=33000m/{{s}^{2}}$
Therefore,
$\begin{aligned} & \Rightarrow F=0.5\times 33000N \\\ & \Rightarrow F=16500N \\\ & \Rightarrow F=16.5\times {{10}^{3}}N \\\ \end{aligned}$
Thus, the force applied by the hero on the baby pig is $16.5\times {{10}^{3}}N$ .

Hence, option $(d)$ is the correct option.

Note:
We have to always remember the value of key figures like, speed of sound, speed of light or any other constant as it may or may not be given in the problem. We also need to be careful regarding the units of different terms and always be sure to check them before including these terms in our calculation.