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:

Options

A. `(5g)/6`
B. `(5g)/3`
C. `(17g)/12`
D. `(17g)/6`

Answer

D

Explanation

`veca_(AB)=(3mg(-hati))/(m+3m)= (3g)/4 (-hati)`
`veca_(CD)=(2mg(-hati))/(m+2m)= (2g)/3 (-hati)`

In a plane mirror the image moves twice as faster as mirror, thus
Acceleration of image in mirror `AB = 2 veca_(AB)`
Acceleration of image in mirror CD `= 2 veca_(CD)`
Acceleration of images w.r.t. each other is
`veca_(xl)=2veca_(CD) -2 veca_(AB)`
`implies veca_(xl) = 2 ((2g)/3) hati-2 ((3g)/4)(-hati)`
`implies veca_(xl) = (17g)/6hati`