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 the box and the surface is $0.15$. The truck starts from rest with an acceleration of $2\, m\, s^{-2}$ on a straight road. The box will fall off the truck when it is at a distance from the starting point equal to

• A. $4\, m$
• B. $8\, m$
• C. $16\, m$
• D. $32\, m$

Answer 1

Answer: (C)

$16\, m$

Answer 2

Maximum acceleration of box = $\mu$g $= 0.15 � 10\, m \,s^{-2} = 1.5\, m\, s^{-2}$ Acceleration of truck, $a_T = 2\, m\, s^{-2}$ Therefore, relative acceleration of the box, $a_r = 0.5\, m\, s^{-2}$ (backwards). It will fall off the truck in a time, $t=\sqrt{\frac{2S}{a_{r}}}=\sqrt{\frac{2\times4}{0.5}}=4\,s$ Displacement of truck upto the instant is, $S_{T}=\frac{1}{2}a_{T}t^{2}=\frac{1}{2}\times2\times\left(4\right)^{2}=16\,m$