Question

A body of mess 10 kg lies on a rough horizontal surface an acceleration of 5 m s${}^{-2}$ and when the horizontal force is doubled, it gets an acceleration of 18 m s${}^{-2}$. Then the coefficient of friction between the body and the horizontal surface is: (assume g = 10 m s${}^{-2}$)

• A. 0.2
• B. 0.8
• C. 0.4
• D. 0.6

Answer 1

The correct option is B 0.8

Given : $m=10$ kg $g=10m/s^2$

Let the horizontal force acting on the body be $F$.

Acceleration of the body $a=5m/s^2$

$\therefore$ $F-f=ma$

Or $F-f=\left(10\right)\left(5\right)=50$ N ....(1)

Now the horizontal force gets doubled i.e. $F^{\prime }=2F$

New acceleration $a^{\prime }=18m/s^2$

$\therefore$ $F^{\prime }-f=m{a}^{\prime }$

Or $2F-f=\left(10\right)\left(18\right)=180$ N ....(2)

Subtracting (1) from (2) we get $F=180-50=130$ N

Putting this in (1), $130-f=50$

We get $f=80$ N

Thus coefficient of friction $\mu =\frac{f}{mg}$

$\therefore$ $\mu =\frac{80}{10\times 10}=0.8$