Question

A block of weight $100N$ is pushed by a force $F$ on a horizontal rough plane moves with an acceleration $1m/s^2$, when force is doubled its acceleration becomes $10m/s^2$. The coefficient of friction is____$(g=10m{s}^{-2})$

• A. $0.2$
• B. $0.4$
• C. $0.8$
• D. $0.5$

Answer 1

The correct option is C $0.8$

Given that,

Weight, $W=100N$

Acceleration, $a=1m/s^2$

Acceleration when force is double, $a=10m/s^2$

Now, Let the External Force be F and friction force be f.

Then,

$F-f_s=ma$

$F-\mu N=ma$

$F-\mu 100=10\times 1$

$F-\mu 100=\mathrm{10....}\left(I\right)$

We know, When Force is doubled,

Then,

$2F-f_s=ma$

$2F-\mu N=ma$

$2F-\mu 100=10\times 10$

$2F-\mu 100=\mathrm{100....}\left(II\right)$

Now, from equation (I) and (II)

$F=90N$

Now, put the value of F in equation (I)

$90-\mu 100=10$

$-\mu 100=10-90$

$\mu =\frac{80}{100}$

$\mu =0.8$

Hence, the coefficient of restitution is $0.8$