A block `B` is placed on the block `A`.The mass of block `B` is less than the mass of block `A`. Friction exists between the blocks , whereas the ground on which block `A` is placed is taken to be smooth. A horizontal force `F`, increasing linearly with time begins to act on `B`. The acceleration `a_(A)` and `a_(B)` of blocks `A` and `B`, respectively , are plotted against `t`. The correctly plotted graph is

Options

A.
B.
C.
D.

Answer

C

Explanation

`F prop t rArr F = kt , k: constant`
(i) When `kt lt mu m_(B) g , mu `: coefficient of friction between the blocks , both the blocks move together with acceleration
`a = (kt)/(m_(A) + m_(B)) = ((k)/(m_(A) + m_(B)))t`
graph `a v//s t : a` straight line with slope `((k)/(m_(A) + m_(B)))`
(ii) When `kt gt mu m_(B)g` , the block moves with different accelerations
`kt - mu m_(B) g = m_(B) a_(B)`
`a_(B) = (k)/(m_(B)) t - mu g` (i)
Graph will be straight line of slope `(k)/(m_(B))` and negative intercept
`mu m_(B) g = m_(A) a_(A)`
`a_(A) = (mu m_(B) g)/(m_(A))` (ii)
Graph will be straight line parallel to time - axis