Two fixed frictionless inclined plane making an angle $3 0^{\circ}$ and $6 0^{\circ}$ with the vertical are shown in the figure. Two block $A$ and $B$ are placed on the two planes. What is the relative vertical acceleration of $A$ with respect to $B$ ?

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m g sin θ = ma ∴ a = g sin θ where a is along the inclined plane ∴ vertical component of acceleration is g sin 2 θ ∴ relative vertical acceleration of A with respect to B is

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