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Question

A small block of mass of 0.1 kg lies on a fixed inclined plane PQ which makes an angle θ with the horizontal. A horizontal force of 1 N acts on the block through its centre of mass as shown in the figure. The block remains stationary if: (take g=10ms2)

A
θ=45
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B
θ>45 and a frictional force acts on the towards P
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C
θ>45 and a frictional force acts on the block towards Q
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D
θ<45 and a frictional force acts on the block towards Q
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Solution

The correct options are
A θ=45
C θ>45 and a frictional force acts on the block towards Q
FBD of the block
Weight of the block
W=0.1(10)=1 N
The net pulling force on the block along the incline is,
F=sin θcos θ, friction acts opposite to net pulling force.

If θ=45F=0 no frictional force is required.
If θ>45sin θ>cos θF is down the incline and friction acts towards Q.
If θ<45sin θ<cos θF is up the incline and friction acts towards P.

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