Question

A rear side of a truck is open and a box of mass 20 kg is placed on the truck 4 metres away from the open end.$\mu =0.15andg=10m/s^2$. The truck starts from rest with an acceleration of $2m/s^2$ on a straight road. The box will fall off the truck when it is at a distance from the starting point equal to :

• A. 4 metres
• B. 8 metres
• C. 16 metres
• D. 32 metres

Answer 1

Answer: (C)

16 metres

Mass of the block $\left(m\right)$=$20$$kg$

Analysing the motion of the block w.r.t. the truck

A pseudo force will be applied on the block in the backward direction=$m\times 2=40N$

Friction will act in the forward direction in order to resist the slipping equal to $\mu mg=30N$

so net force will act in backward direction equal to $10N$

So, acceleration in the backward direction w.r.t. the truck=$10/20$=$0.5$

The displacement of the block w.r.t. the truck when it will fall down=$4m$

Let the time taken be '$t$'

Therefore, $4=\frac{1}{2}\times \frac{1}{2}\times t^2\Rightarrow t=4sec.$

Distance travelled by the truck w.r.t. the ground=$\frac{1}{2}\times 2\times 4^2=16m$