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Question

A circular disc with a groove along its diameter is placed horizontally. A block of mass 1 kg is placed as shown. The coefficient of friction between the block and all surfaces of groove in contact is μ=25. The disc has an acceleration of 25 m/s2 Find the acceleration of the block with respect to disc.

A
10 m/s2
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B
20 m/s2
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C
15 m/s2
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D
5 m/s2
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Solution

The correct option is A 10 m/s2
Since the disk is a non inertial frame, a pseudo forces will act towards the right direction on the block.

Normal reaction in vertical direction N1=mg
Normal reaction from side to the groove N2=masin37
Now, the balance the force along the groove
mar=macos37μN1μN2 [where N1=mg, N2=masin37 ]
Therefore, acceleration of block with respect to disc
ar=macos37μN1μN2m
Substituting the values we get,
ar=1×25×cos3725×1×1025×25×sin371
ar=10 m/s2

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