In order to raise a mass of 100 kg, a man of mass 60 kg fastens a rope to it and passes the rope over a smooth pulley. He climbs the rope with acceleration `5g//4` relative to the rope. The tension in the rope is (take `g=10 ms^(-2)`)

Options

A. `(4875)/(8)N`
B. `(4875)/(2)N`
C. `(4875)/(4)N`
D. `(4875)/(6)N`

Answer

C

Explanation

Let T be the tension in the rope and a the acceleration of rope.
The absolute acceleration of man is, therefore, `((5g)/(4)-a)`.
Equation of motion for mass and man gives:
`T-100g=100a` ..(i)
`T-60g=60((5g)/(4)-a)`…(ii)
Solving Eqs(i) and (ii) we get `T=(4875)/(4)N`.