Question

A body of mass 10 kg lies on a rough horizontal surface. When a horizontal force of F newtons acts on it, it gets an acceleration of $5m/s^2$. And when the horizontal force is doubled, it gets an acceleration of $18m/s^2$. The coefficient of friction between the body and the horizontal surface is (Take $g=10m/s^2$)

• A. 0.2
• B. 0.4
• C. 0.6
• D. 0.8

Answer 1

Answer: (D)

0.8

Let the coefficient of friction be $\mu$.
Normal Force, $N=mg$
Therefore frictional force $f=\mu mg$
When force is $F$:
Acceleration $a=\frac{F-f}{m}$
$\Rightarrow 5m=F-f$
When force is $2F$:
Acceleration $a=\frac{2F-f}{m}$
$\Rightarrow 18m=2F-f$
Comparing both equations and eliminating $F$:
$10m=2F-2f18m=2F-f\Rightarrow 8m=f=\mu mg\Rightarrow 8=\mu g\Rightarrow \mu =8/10=0.8$