Question

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

• A. $14$m
• B. $8$m
• C. $82$m
• D. $16$m

Answer 1

Answer: (D)

$16$m

The maximum acceleration of box is
$a_{max}=\mu g=0.15\times 10=1.5m/s^2$
Given acceleration of truck $=a=2m/s^2$
So, net acceleration of box is
$a_{net}=a-a_{max}=2-1.5=0.5m/s^2$
The box will fall off the truck in time
$t=\sqrt{\frac{2l}{a_{net}}}=\sqrt{\frac{2\times 4}{0.5}}=4s$
Now, the displacement of truck for this instant is
$S_t=\frac{1}{2}{a}_t\cdot t^2$
$=\frac{1}{2}\times 2\times 4^2=16$m.