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. `g//3`
D. `17g//6`

Answer

B

Explanation

acc of block A
`rArr a_(A) = (3m-m)/(4m) xx g = g//2`
`:.` acc of image in A mirror `=- 2g//2hai I =- g hati` Similary acc of block C
`a_(C) = (2m-m)/(3m) xx g = g//3`
`:.` acc of image in C mirror `= 2 xx (g//3hati) = 2g//3 hati`
Image acceleration w.r.t. to each other
`:. |vec(a)_(A//C) = |vec(a)_(A-)vec(a)_(C)| = |-g hati - 2g//3 hati| = 5g//3`