Solveeit Logo
Login

Question

Question: A block of mass m is placed on a wedge of mass M. coefficient between then is μ\<cot θ. The wedge is...

A block of mass m is placed on a wedge of mass M. coefficient between then is μ<cot θ. The wedge is given an acceleration to its left. Find the maximum acceleration at which block appears stationary relative to wedge.

A

g(sin⁡θ−μcos⁡θ)cos⁡θ+μsin⁡θ\frac { g ( \sin \theta - \mu \cos \theta ) } { \cos \theta + \mu \sin \theta }

B

g(sin⁡θ+μcos⁡θ)cos⁡θ−μsin⁡θ\frac { g ( \sin \theta + \mu \cos \theta ) } { \cos \theta - \mu \sin \theta }

C

g(cos⁡θ+μsin⁡θ)sin⁡θ−μcos⁡θ\frac { g ( \cos \theta + \mu \sin \theta ) } { \sin \theta - \mu \cos \theta }

D

None of these

Answer

g(sin⁡θ+μcos⁡θ)cos⁡θ−μsin⁡θ\frac { g ( \sin \theta + \mu \cos \theta ) } { \cos \theta - \mu \sin \theta }

Explanation

Solution

N = m(g cos θ + a sin θ)

ma cos θ = mg sin θ + μN

ma cos θ = mg sin θ + μ mg cos θ + μ ma sin θ

ma (cos θ μ sin θ) = mg sinθ + mg cos θ

or a = g(sin⁡θ+μcos⁡θ)cos⁡θ−μsin⁡θ\frac { g ( \sin \theta + \mu \cos \theta ) } { \cos \theta - \mu \sin \theta }