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Q.

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 & CD of the two blocks are made reflecting. The acceleration of two images formed in those two reflecting surfaces w.r.t. each other is:

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a

5g / 6

b

5g/3

c

g/3

d

17g / 6

answer is D.

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Detailed Solution

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Acceleration of mirror ‘C’ is
$a_{C} = \frac{2 mg}{2 m + m} = \frac{2 g}{3}$

Acceleration of mirror ‘A’ is
$a_{A} = \frac{3 mg}{3 m + m} = \frac{3 g}{4}$
Accelerations of images in those mirrors are
$a_{C}^{I} = 2 a_{C} = \frac{4 g}{3}$
$a_{A}^{I} = 2 a_{A} = 3 g / 2 . As a_{C}^{I}, a_{A}^{I}$ are in opposite direction, relative acceleration between the images is
$a = \frac{4 g}{3} + \frac{3 g}{2} = \frac{17 g}{6}$

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