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  • A small mass m is slipping over a frictionless incline made of wood of mass M .The acceleration by which the incline should be pushed so that block m remains stationary  w.r.t incline is 

A small mass m is slipping over a frictionless incline made of wood of mass M .The acceleration by which the incline should be pushed so that block m remains stationary  w.r.t incline is  

Option: 1

\frac{2}{\sqrt 3 }g


Option: 2

\frac{g}{\sqrt 3 }


Option: 3

\frac{g}{\sqrt 2 }


Option: 4

\frac{\sqrt 3}{2}g


Answers (1)

best_answer

Solution-

Let the acceleretiom of triangular wedge be 'a', as shown in the figure.

As the block remains stationary with respect to the wedge, the block should be in equilibrium in frame of referece of the wedge.

F.B.D in the frame of reference attached with the wedge along the incline-

Note- Since the frame of reference is accelerated (non-inertial), a pseudo force (ma) acts on the block towards the left.

Applying condition of equilibrium along the incline-

macos30^0=mgsin30^0\\ a=gtan30^0\\ \Rightarrow a=\frac{g}{\sqrt{3}}

 macos\theta=mgsin\theta\\ a=gtan\theta=gtan30^o=\frac{g}{\sqrt3}  

Posted by

Pankaj

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