A mass M is placed on a smooth wedge of angle | vedclass

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(D) To keep the mass $M$ at rest relative to the wedge,we analyze the forces in the non-inertial frame of the wedge.When the wedge accelerates to the

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$a$ is applied to the left and $a=g 	an 	heta$

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(D) To keep the mass $M$ at rest relative to the wedge,we analyze the forces in the non-inertial frame of the wedge.When the wedge accelerates to the left with acceleration $a$,a pseudo force $F_p = Ma$ acts on the mass $M$ towards the right.The forces acting on the mass $M$ along the incline are:$1$. The component of pseudo force $Ma \cos 	heta$ acting up the incline.$2$. The component of gravitational force $Mg \sin 	heta$ acting down the incline.For the mass to remain at rest relative to the wedge,these two forces must balance:$Ma \cos 	heta = Mg \sin 	heta$$a \cos 	heta = g \sin 	heta$$a = g \frac{\sin 	heta}{\cos 	heta}$$a = g 	an 	heta$Thus,an acceleration $a = g 	an 	heta$ must be applied to the wedge towards the left.

$A$ mass $M$ is placed on a smooth wedge of angle $\theta$ resting on a frictionless surface. To keep the mass $M$ at rest relative to the wedge,the wedge must be given a horizontal acceleration $a$ equal to:

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