Question

A block of mass $10kg$ is placed at a distance of $5m$ from the rear end of a long trolley as shown in the figure. The coefficient of friction between the block and the surface below is $0.2$. Starting from rest, the trolley is given a uniform acceleration of $3m{s}^{-2}$. At what distance from the starting point will the block fall off the trolley (Take $g=10m{s}^{-2})$

• A. 15 m
• B. 20 m
• C. 25 m
• D. 30 m

Answer 1

The correct option is A 15 m

Pseudoforce on block $F=10\times 3=30N$
Frictional force on block $f=\mu mg=0.2\times 10\times 10=20N$
Acceleration of block with respect to trolley
$a=\frac{F-f}{m}$
$=\frac{30-20}{10}=1m/s^2$
If the block falls from trolley after time 't'
$S=\frac{1}{2}a{t}^2$
$5=\frac{1}{2}\times 1\times t^2\Rightarrow t=\sqrt{10}s$
displacement of trolley in $\sqrt{10}$ s
$S^{\prime }=\frac{1}{2}\times 3\times 10=15m$