A circular disc with a groove along its diameter is placed horizontally. A block of mass 1 kg is placed as shown. The co-efficient of friction between the block and all surfaces of groove in contact is $μ = 2 / 5$ The disc has an acceleration of $25 m / s^{2}$ Find the acceleration of the block with respect to disc.

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Solution

Since the disk is a non inertial frame, we have to apply pseudo forces if we want to see the motion of the block wrt the disk.
Hence, pseudo force on the block towards right direction is 1 kg multiplied by 25 $m / s^{2}$ equals 25 N.

Along the diameter it will be 25 $c o s θ$ $=$ 20 N.
The normal force between the block and the mass is 25 $s i n θ$ $=$ 15 N.
Hence the frictional force will be 15x $\frac{2}{5}$ $=$ 6 N.
So the force along the axis is (20-6) $=$ 14 N.
Hence acceleration $=$ 14 $m / s^{2}$

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