A varying horizental force `F =at` act on a block of mass `m` kept on a smooth horizontal surface An identical block is kept on the first block.The coefficient of friction between the blocks is `mu` . The time after which the relative sliding between the blocks prevails is

Options

A. `(2 m g)/(a)`
B. `(2 mu m g)/(a)`
C. `(mu m g)/(a)`
D. `2 mu mga`

Answer

B

Explanation

Maximum friction between two ,
`f_(max) = mu N = mu mg`
upper block moves only due to friction. Therefore its acceleration may be,
`a_(max) = (f_(max)/(m) = mu g`
Relative motion between them will start when common acceleration becomes `mu g`
`:. mu g = ("Net force")/("Total mass") = ("at")/(2m)`
`t = (2mu mg)/(a)`