Question

An object kept on a smooth inclined plane of inclination $\theta$ with horizontal can be kept stationary relative to the incline by giving a horizontal acceleration to the inclined plane, equal to :

• A. g sin $\theta$
• B. g cos $\theta$
• C. g tan $\theta$
• D. None of these

Answer 1

The correct option is C g tan $\theta$

let us assume acceleration of wedge in rightward direction. Then FBD of block with respect to wedge is drawn in the figure which include pseudo force due to acceleration of wedge.

so component of pseudo force in the direction parallel to the wedge surface will balance the gravitational force of the block.

i.e. $maCos\theta =mgSin\theta$

=>$a=Tan\theta$

so option C is best possible answer.