Question

An object of mass $m$ is projected on the rough horizontal surface of coefficient of friction $\mu$ with some initial K.E. The time $t$ taken before stopping is:
a. $t$ $\alpha$ $\mu$
b. $t$ $\alpha$ $\frac{1}{\sqrt{m}}$
c. $t$ $\alpha$ $m$
d. $t\alpha \frac{1}{\mu }$

• A. Both a & b are correct
• B. Both a & c are correct
• C. Both b & d are correct
• D. Both c & d are correct

Answer 1

Answer: (C)

Both b & d are correct

Let $u$ be the initial velocity of the body.
Kinetic Energy, $KE=\frac{1}{2}m{u}^2$
$\Rightarrow u=\sqrt{\frac{2KE}{m}}$
Frictional force will act as a retarding force, $F=\mu mg$
Therefore, the deceleration of the body is $\mu g$
From,
$v=u+at$
$\Rightarrow 0=u-\mu gt$
$\Rightarrow t=\frac{u}{\mu g}=\frac{\sqrt{2KE}}{\sqrt{m}\mu g}$
So,
$t\propto \frac{1}{\sqrt{m}}$
$t\propto \frac{1}{\mu }$