A block of mass m and length l is kept at rest on a rough horizontal ground of friction coefficient `mu_(k)`. A man of mass m is standing at the right end. Now the man starts walking towards left and reaches the left end within time ‘t’. During this time, the displacement of the block is : (Assume the pressing force between the block and the ground remains constant and its value is same as it was initially. Also as sume that the block slides during the entire time (t))

Options

A. `(l-mu_(k) g t^(2))/2`
B. `(l+mu_(k) g t^(2))/2`
C. `(mu_(k) g t^(2)-l)/2`
D. `l/2`

Explanation

`(F_("net"))_("ext")=mu_(k)(2m)g=m_("total")a_(cm)`
`a_(cm)=mu_(k)g`
`S_(cm)=0+1/2(mu_(k)g)t^(2)`
`S_(cm)=(m_(1)S_(1)+m_(2)S_(2))/(m_(1)+m_(2))`
`-1/2 (mu_(k)g)t^(2)=((m)(x)+(m)(x-l))/(m+m)`
`x=(l-(mu_(k)g)t^(2))/2`