Question

The rear side of a truck is open and a box of mass $20\text{kg}$ is placed on the truck $4\text{m}$ away from the open end. The coefficient of friction between the box and the surface is $0.15$. The truck starts from rest with an acceleration of $2{\text{m s}}^{-2}$ on a straight road. The box will fall off the truck when it is at a distance from the starting point equal to (take $g=10m{s}^{-2}$)

• A. $4\text{m}$
• B. $8\text{m}$
• C. $16\text{m}$
• D. $32\text{m}$

Answer 1

The correct option is C $16\text{m}$

Maximum acceleration of box $=\mu g$
$=0.15\times 10{\text{ms}}^{-2}=1.5{\text{m s}}^{-2}$
Acceleration of truck, $a_T=2{\text{m s}}^{-2}$
Therefore, relative acceleration of the box,
$a_r=0.5{\text{m s}}^{-2}$ (backwards)
It will fall off the truck in a time,
$t=\sqrt{\frac{2S}{a_r}}=\sqrt{\frac{2\times 4}{0.5}}=4\text{s}$
Displacement of truck upto the instant is,
$S_T=\frac{1}{2}{a}_T{t}^2=\frac{1}{2}\times 2\times (4{)}^2=16\text{m}$