A monkey of mass `'m'` climbs up to a rope hung over a fixed pulley with an acceleration `g//4`. The opposite end of the rope is tied to a block of mass `M` lying on a rough horizontal plane. The coefficient of friction between the block and horizontal plane is `mu`. Find the tension in the rope.

Explanation

`a_("monkey"//"rope")=g//4`
Let acceleration of `M=a_(0)`
So, acceleration of rope `=a_(0)`
`veca_("monkey")=veca_("monkey"//"rope")+veca_("rope")=(a_(0)-g//4)`
Now for mass `M`, `T-mu Mg=Ma_(0)`……(`1`)
For monkey `mg-T=m(a_(0)-g//4)`......(`2`)
From equation (`1`) and (`2`)
`mg-mu Mg=a_(0)(M+m)-(mg)/(4)`
`rArr a_(0)=((5m)/(4)-muM)g//(M+m)=((5m-4muM)g)/(4(M+m))`
`:. T=(M(5m-4mu M)g)/(4(M+m))+mu Mg`