In the figure shown a block B of mass m can slide on a fixed horizontal smooth plane. A solid sphere A of radius r of the same mass rolls without sliding on the block B. The angular acceleration of the sphere is 10g/xr where ‘x’ is _______

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Detailed Solution

$a_{2} + Rα = a_{1} \dots \dots \dots . . (1)$

$2 mg - f = {ma}_{1} \dots . . (2)$

$f = {ma}_{2} \dots \dots . . (3)$

$\frac{2}{5} {mR}^{2} α = fR; f = \frac{2}{5} mRα$

$2 mg - \frac{2}{5} mRα = {ma}_{1}$

$\Rightarrow a_{1} = 2 g - \frac{2}{5} {Rαa}_{2} = \frac{2}{5} Rα (1)$

$\Rightarrow \frac{2}{5} Rα + Rα = 2 g - \frac{2}{5} Rα$

$\Rightarrow \frac{9}{5} Rα = 2 g \Rightarrow α = \frac{10 g}{9 R}$

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