Question

A trolley carries a body of weight $25kg$. which is kept at a distance of $2.5m$ from the rear end of the trolley. The trolley starts from rest and accelerates at a constant rate of $2m{s}^{-2}$ If the coefficient of friction between the trolley and the body is $0.1$, find the distance of the trolley from the starting point where the body will just slip out of the trolley. $\text{Take}g=10m{s}^{-2}$

• A. $4m$
• B. $3m$
• C. $5m$
• D. $10m$

Answer 1

The correct option is C $5m$

The force which moves the body is the frictional force.
$f_{max}=\mu mg\Rightarrow a_{max}=\mu g=0.1\times 10$
$=1m{s}^{-2}<2m{s}^{-2}$
$\Rightarrow slipping$
Relative acceleration $=2-1=1m{s}^{-2}$
$2.5=0\times t+\frac{1}{2}\times 1\times t^2\Rightarrow t^2=5\Rightarrow t=\sqrt{5}s$
Distance travelled by the trolley in this time $s=ut+\frac{1}{2}a{t}^2=0+\frac{1}{2}\times 2\times 5=5m$