An object kept on smooth inclined plane of 1 in L  can be kept stationary relative to the incline by giving a acceleration to the incline by

 

Ans gtan

 

I want a detailed ans

 

i prms to rte u fr helping me

Let angle of the inclined plane with the horizontal be =

 

Now if an object of mass 'm' is kept on the plane.

 

Then component of gravitational force along the plane = mg sin, down the plane

 

Now if the system is accelerated by 'a' then pseudo force on the object = ma, in the horizontal direction.

 

Also the component of this force along the plane = ma cos (along the plane but opposite to the component of gravitational force.

 

Thus for equilibrium of particle to occur

 

mg sin =ma cos

 

or a = g tan