A block of mass m is resting one a smooth horizontal surface. One end of a uniform rope of mass m/3 is fixed to the block, which is pulled in the horizontal direction by applying force F at the other end. The tension in the middle of the rope is

Options

A. `(8)/(6)F `
B. `(1)/(7)F`
C. `(1)/(8)F`
D. `(7)/(8)F`

Answer

D

Explanation

Acceleration of the system.
`a = (F)/((m+(m)/(3)))`
`therefore` Tension in the middle of the rope is
`T = (m+(m)/(6))a`
or`T = (7m)/(6)*(3F)/(4m) = (7)/(6)F`