Question

A block of mass 10 kg is placed at a distance of 5 m from rear end of a long trolley as shown. 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 of the trolley ? (take $g=10m{s}^{{}^{-2}})$

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

Answer 1

The correct option is A $15m$

Force on block $F=ma=30N$
$f=\mu mg=0.2\times 10\times 10=20N$

$\therefore$ Net force on block towards right
$F^1=F-f=30-20=10N$

Due to friction block experiences an acceleration towards rear end
$a^1=\frac{F^1}{m}=\frac{10}{10}=1m{s}^{-2}$

Dist. travelled : $S=ut+\frac{1}{2}a{t}^2$

Putting, $S=5m,u=0;a=a^1=1m{s}^{-2}$ gives:
$t=\sqrt{10}$
$\therefore S^1=ut+\frac{1}{2}a{t}^2$
$=0+\frac{1}{2}\times 3\times {\left(\sqrt{10}\right)}^2=15m$