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Question

Two blocks A and B of masses mA=1 kg and mB=2 kg are placed in contact on a frictionless plane of inclination 30. Find the magnitude of contact force between the two blocks when an external force is applied on the blocks as shown in the figure.

A
2 N
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B
6 N
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C
12 N
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D
10 N
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Solution

The correct option is D 10 N
We can consider both the blocks as a system of 3 kg as they move same acceleration.
F.B.D of the system will be

From FBD, we can write
Fcos30mgsin30=ma
203×3230×12=3a
a=5 m/s2 (i)
Let N be the contact force between the two blocks.
Now, FBD of 1 kg block will be

From FBD, we can say
Ngsin30=1×a (ii)
Using equation (i) in (ii), we get
N5=5
N=10 N


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