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Question

Three blocks are placed on a smooth inclined plane with force acting on m1 parallel to the inclined plane. Find the contact force between m2 and m3.


A
(m1+m2+m3)Fm3
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B
m3Fm1+m2+m3
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C
F(m1+m2)g
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D
None of these
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Solution

The correct option is B m3Fm1+m2+m3
Analysing the motion of (m1+m2+m3) as a system,
Acceleration of the system, a=Net pushing forceTotal mass
=F(m1+m2+m3)gsin θm1+m2+m3(i)

Let N be the contact force between blocks m2 and m3.
Drawing FBD of m3 and analysing its motion,

Using the above figure, we can write
Nm3gsinθ=m3a(ii)

Using equation (i) in (ii), we get
N=m3 g sin θ+m3[F(m1+m2+m3)gsinθm1+m2+m3]
N=m3Fm1+m2+m3

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