A block `A` of mass `m` is over a plank `B` of mass `2m`. Plank `B` si placed over a smooth horizontal surface. The coefficient of friction between `A` and `B` is `(1)/(2)`. Blocks `A` is given a velocity `V_(0)` towards right. Then

Options

A. Acceleration of `A` is `(g)/(2)`
B. Acceleration of `A` is `g`
C. Acceleration of `B` relative to `A` is `(3)/(4)g`
D. Acceleration of `A` is zero

Answer

A, C

Explanation

Force of friction between the two will be maximum i.e., `mu mg`
Retardation of `A` is `a_(A) = (mu mg)/(m) = mu g`
and acceleration of `B` is `a_(B) = (mu mg)/(2m) = (mu g)/(2)`
`therefore` Acceleration of `B` relative to `A` is
`a_(BA) = a_(A)+a_(B) = (3 mu g)/(2)` substituting `mu = (1)/(2)a_(BA) = (3g)/(4)`.