A circular disc with a groove along its diameter is placed horizontally on a rough surface. A block of mass 1 kg is placed as shown .The co-efficient of friction between the block and all surfaces of groove and horizontal surface in contact is $μ= \frac{2}{5}$ . The disc has an acceleration of ${25m/s}^{2}$ towards left. The acceleration $({in m/s}^{2})$ of the block with respect to disc is 5x find the x value (Given $cosθ= \frac{4}{5},sinθ= \frac{3}{5}$ )

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Detailed Solution

Applying pseudo –force ma and resolving it Applying $F_{n e t} = m α_{x}$ for x direction

$m a \cos θ - (f_{1} + f_{2}) = m a_{x}$

$m α \cos θ - μ N_{1} - μ N_{2} = m α_{x}$

$m α \cos θ - μ m α \sin θ - μ m g = m α_{x}$

$\Rightarrow α_{x} = α \cos θ - μ α \sin θ - μ g$

$= 25 \times \frac{4}{5} - \frac{2}{5} \times 25 \times \frac{3}{5} - \frac{2}{5} \times 10 = 10 m / s^{2}$

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