1. Tardigrade
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  4. A triangular block of mass M with angles 30°, 60° and 90° rests with its 30°-90° side on a horizontal table. A cubical block of mass m rests on the 60°-30° . The acceleration which M must have relative to the table to keep m stationary relative to the triangular block assuming frictionless contact is

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Q. A triangular block of mass $M$ with angles $30^{\circ}, 60^{\circ}$ and $90^{\circ}$ rests with its $30^{\circ}-90^{\circ}$ side on a horizontal table. A cubical block of mass $m$ rests on the $60^{\circ}-30^{\circ} .$ The acceleration which $M$ must have relative to the table to keep $m$ stationary relative to the triangular block assuming frictionless contact is

Laws of Motion

Solution:

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When $M$ is accelerated with acceleration $a$, pseudo force $m a$ acts on the block $m$. The ' $m a$ ' can be resolved as $m a$ $\cos 30^{\circ}$ along the inclined plane and $m a \sin 30^{\circ}$ normal to it.
For 0 acceleration of block $m$ w.r.t. $M$
$m g \sin 30^{\circ}-m a \cos 30^{\circ}=0 \Rightarrow a=g \tan 30^{\circ}=\frac{g}{\sqrt{3}}$