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

Options

A. 4m
B. 8m
C. 16m
D. 32m

Answer

A

Explanation

(a) Maximum acceleration of the box can be `mu g`or `1.5 ms^(-2)`, while acceleration of truck is `2ms^(-2)`.Therefore, relative acceleration of the box will be`a_(r)=0.5 ms^(-2)`(backward).It will fall off the truck in a time.
`t=sqrt((2l)/(a_(r)))" "(s=(1)/(2)at^(2))`
`=sqrt((2xx4)/(0.5))=4 s`
Displacement of truck upto this instant is ,
`s_(r)=(1)/(2)a_(r)t^(2)=(1)/(2)xx05xx(4)^(2)=4m`