Two block of same mass'm' are joined with an dideal spring of spring constant k and sept on a rough surface as shown in figure. The spring is initially unstretched and coefficient of friction between the blocks and horizontal surface is `mu` and `2 mu` respectively. What should be the maximum speed of block 'A' such that the block 'B' does not move ?

Options

A. `2mug sqrt((2m)/(k))`
B. `mugsqrt((2m)/(k))`
C. `mug sqrt((m)/(k))`
D. `2 mug sqrt((m)/(2k))`

Answer

A

Explanation

`(1)/(2)mv^(2) = mumgx + (1)/(2) kx^(2)` ….(i)
`2mumg = kx` …..(ii)
From (i) and (ii)
`v = mug sqrt((8m)/(k)) = 2mug sqrt((2m)/(k))`