Question

A block od mass 10 kg is moving up an inclined plane of inclination ${30}^o$ with an initial speed of 5 m/s. It stopes after 0.5 s, what is the value of coefficient of kinetic friction?

• A. $0.5$
• B. $0.6$
• C. $\sqrt{3}$
• D. $\frac{1}{\sqrt{3}}$

Answer 1

The correct option is D $\frac{1}{\sqrt{3}}$

Two force acting on the block force due to gravity and friction force as shown in the figure.

$f=\mu mgcos\theta =\mu 50\sqrt{3}$

$F_g=mgsin\theta =100sin{30}^0=50N$

acceration due to force on the block is a

$F_g+f=ma$

$\Rightarrow 50N+\mu 50\sqrt{3}=10a$

$\Rightarrow a=5+5\sqrt{3}\mu$ ...eq(1)

block has a velocity $v=5m{s}^{-1}$ upword the inclined plane.

it retard and stop after some time

using eq of kinetic motion

$v=u+at$

$\Rightarrow 5=a\times .5$

$\Rightarrow a=10m{s}^{-2}$

using eq(1) we get \mu

$5+5\sqrt{3}\mu =10$

$\Rightarrow \mu =\frac{1}{\sqrt{3}}$

Hence D option is correct.