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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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A small cubical block of mass 1 kg is placed inside a rough rectangular groove μ=12 made in a circular table as shown in the figure. The table starts rotating with angular acceleration 1rads2 in a horizontal plane about its axis. The time 10Ksec after which the blocks will start motion with respect to the table. Find the value of K. (Take g=10m/s2) Assume the size of block slightly smaller than the width of the groove.


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