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

Answer

D

Explanation

The acceleration of the system is
` a=(F)/(m +(m)/(6))=(3F)/(4m)`

The tension in the middle of the rope (i.e., at point A) is

` T=(m+(m)/(6)) a =(7m)/(6) xx(3F )/(4m)`
`or T=(7)/(8) F `