In the adjoining figure,if the acceleration o | vedclass

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(B) Let $\vec{a}_M$ be the acceleration of the wedge $M$ with respect to the ground,where $|\vec{a}_M| = a$.Let $\vec{a}_{m/M}$ be the acceleration of

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acceleration of $m$ with respect to ground is $2a \sin(\alpha/2)$

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(B) Let $\vec{a}_M$ be the acceleration of the wedge $M$ with respect to the ground,where $|\vec{a}_M| = a$.Let $\vec{a}_{m/M}$ be the acceleration of block $m$ with respect to the wedge $M$. Since the string is inextensible and the pulley is fixed to the wedge,the magnitude of acceleration of $m$ relative to the wedge is also $a$ (directed along the incline).The acceleration of $m$ with respect to the ground is $\vec{a}_m = \vec{a}_{m/M} + \vec{a}_M$.The angle between $\vec{a}_{m/M}$ and $\vec{a}_M$ is $(\pi - \alpha)$.Using the law of vector addition,the magnitude is $a_m = \sqrt{a^2 + a^2 + 2a^2 \cos(\pi - \alpha)}$.Since $\cos(\pi - \alpha) = -\cos \alpha$,we have $a_m = \sqrt{2a^2(1 - \cos \alpha)}$.Using the identity $1 - \cos \alpha = 2 \sin^2(\alpha/2)$,we get $a_m = \sqrt{2a^2 \cdot 2 \sin^2(\alpha/2)} = 2a \sin(\alpha/2)$.

In the adjoining figure,if the acceleration of the wedge $M$ with respect to the ground is $a$,then:

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