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Question

# Figure shows a wedge of mass 2 kg resting on a frictionless floor. A block of mass 1 kg is kept on the frictionless wedge and the wedge is given an acceleration of 5 m/s2 towards right. Then select the correct statement. (Assume g=10 m/s2)

A
the block will remain stationary w.r.t wedge
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B
the block will have an acceleration of 1 m/s2 w.r.t wedge
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C
the normal reaction on the block is 11 N
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D
None of the above
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Solution

## The correct option is C the normal reaction on the block is 11 NIn the Non-inertial frame of wedge and block, we have F.B.D. of 1 kg block. After resolving the forces, a) Resolving forces along the wedge surface, F=mgsinθ−macosθ ⇒ F=mgsin37∘−macos37∘ ⇒ F=1×10×35−1×5×45 ⇒ F=2 N Hence, 1 kg block will not be stationary because of 2 N force. b) F=ma (block is allowed to move only along the wedge surface) We got F=2 N along the wedge surface, so acceleration of the block w.r.t wedge F=ma⇒2=1×a ⇒a=2 m/s2 c) N=mgcosθ+masinθ ⇒N=mgcos37∘+masin37∘ ⇒N=1×10×45+1×5×35 ⇒N=11 N ∴ Normal force =11 N Hence, option (c) is correct.

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