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Question

Find F such that the 2 kg body goes up with an acceleration of 2 m/s2.
Take (g=10 m/s2)

A
10 N
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B
20 N
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C
25 N
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D
30 N
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Solution

The correct option is D 30 N
FBDs of the two bodies are as shown.

For 2 kg block, we can write
T2g=2a
T=2(a+g)=2(2+10)=2(12)=24 N
For 3 kg block, we can write
FT=3a
F=T+3a
F=24+3(2)=30
Thus, F=30 N

Alternate:
Consider the two bodies as a system whose acceleration is 2 m/s2, so the effective force is on the left side.


So, for equilibrium we have
a=(Effective force)Total mass=F2g5
2=F2g5F=10+2g=10+2×10
Thus, F=30 N

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