Solveeit Logo
Login

Question

Question: A block of mass m rests on a rough horizontal surface with a rope tied to it. The co-efficient of fr...

A block of mass m rests on a rough horizontal surface with a rope tied to it. The co-efficient of friction between the surface and the block is m. A monkey of the same mass climbs at the free end of the rope. The maximum acceleration with which the monkey can climb without moving the block is-

A

μgμsin⁡θ+cos⁡θ−g\frac { \mu g } { \mu \sin \theta + \cos \theta } - g

B

μgμsin⁡θ−cos⁡θ+g\frac { \mu g } { \mu \sin \theta - \cos \theta } + g

C

μgtan⁡θ−μcos⁡θ+g\frac { \mu g } { \tan \theta - \mu \cos \theta } + g

D

μgtan⁡θ+μsec⁡θ−g\frac { \mu \mathrm { g } } { \tan \theta + \mu \sec \theta } - \mathrm { g }

Answer

μgμsin⁡θ+cos⁡θ−g\frac { \mu g } { \mu \sin \theta + \cos \theta } - g

Explanation

Solution

T – mg = ma ……(1)

T cos q = m (mg – T sinq)

T=μmg(cos⁡θ+μsin⁡θ)\mathrm { T } = \frac { \mu \mathrm { mg } } { ( \cos \theta + \mu \sin \theta ) }

a=μg(cos⁡θ+μsin⁡θ)a = \frac { \mu g } { ( \cos \theta + \mu \sin \theta ) }