Two blocks each of mass m lie on a smooth table. They are attached to two other masses as shown in the figure. The pulleys and strings are light. An object O is kept at rest on the table. The sides AB and CD of the two blocks are made reflecting. The acceleration of two images formed in these two reflecting surfaces w.r.t. each other is $\frac{17 g}{p}$ then find the value of $p$ .

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answer is B.

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Detailed Solution

$\begin{array}{l} Acceleration of block AB = \frac{3 mg}{3 m + m} = \frac{3}{4} g \\ Acceleration of block CD = \frac{2 mg}{2 m + m} = \frac{2 g}{3} \\ Acceleration of image in mirror AB = 2 \times acceleration of mirror = 2 (\frac{- 3 g}{4}) = \frac{- 3}{2} g \\ Acceleration of image in mirror CD = 2 (\frac{2 g}{3}) = \frac{4 g}{3} \\ ∴ Acceleration of the two images w.r.t. each other = \frac{4 g}{3} - (\frac{- 3 g}{2}) = \frac{17 g}{6} \end{array}$