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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 $μ = \frac{2}{5},$ the disc has an acceleration of $25 m / s^{2} .$ Find the acceleration of block with respect to disc

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$10 m / s^{2}$

$5 m / s^{2}$

$20 m / s^{2}$

$1 m / s^{2}$

answer is A.

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Detailed Solution

Making FBD of block with respect to disc.
Let a be the acceleration of block with respect to disc

$N_{1} = m g$

$N_{2} = m a \sin θ$

$A = \frac{m a \cos θ - μ N_{2} - μ N_{1}}{m} = 10 m / s^{2}$

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