In the given figure,

Options

A. acceleration of `m_(1)` and `m_(2)` are same
B. the magnitude of relative acceleration of `m_(1)` with respect to `m_(2)` is twice the magnitude of acceleration of `m_(1)`
C. the velocities of `m_(1)` and `m_(2)` are same
D. the speed of `m_(1)` and `m_(2)` are not same

Answer

B

Explanation

`x_(1)+x_(2)=l` (length of string)
`(dx_(1))/(dt)+(dx_(2))/(dt)=0`
`v_(1)+v_(2)=0`
`implies " "v_(1)=-v_(2)`
and `a_(1)=-a_(2)`
`a_(m_(1)m_(2))=a_(m_(1))-a_(m_(2))`
`=a-(-a)=2a`