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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 s2 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=10 ms2)

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

The correct option is C 16 m
Maximum acceleration of box =μg
=0.15×10 ms2=1.5 m s2
Acceleration of truck, aT=2 m s2
Therefore, relative acceleration of the box,
ar=0.5 m s2 (backwards)
It will fall off the truck in a time,
t=2Sar=2×40.5=4 s
Displacement of truck upto the instant is,
ST=12aTt2=12×2×(4)2=16 m

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