A block A of mass `2 kg` is placed over smooth block B of mass `4 kg` which is placed over a smooth horizontal floor The coefficient of friction between A and B is `0.4` when a horizontal forces of magnitude `10 N` is applied on A the acceleration of block of A and B are

Options

A. ` 1 ms^(-2) and 2ms^(-2)`,respectively
B. ` 5 ms^(-2) and 2.5ms^(-2)`,respectively
C. Both the block will moves together with acceleration `1//3 ms^(-2)`
D. Both the block will moves together with acceleration `5//3 ms^(-2)`

Answer

d

Explanation

If the block move together
`a = (F)/(m_(A) + m_(B)) = (10)/(6) = (5)/(3)ms^(-1)`
`f_(B) `(frictional force on B)`= m_(B)a = (m_(B)F)/(m_(A) + m_(B)) = (20)/(3) N`
`f_(max) = mu m_(B)= 0.4 xx 2 xx 10 = 8 N`
As `f_(B max) gt f_(B)` the block will not be seperated and move together with common acceleration `5//3ms^(-2)`