A small block is in contact with the smooth underside of an inclined surface making angle θ with the horizontal. The support accelerates horizontally so that the pseudo force tends to keep the block pressed against the underside. The critical horizontal acceleration at which the normal reaction just becomes zero is:
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Question

A small block is in contact with the smooth underside of an inclined surface making angle θ with the horizontal. The support accelerates horizontally so that the pseudo force tends to keep the block pressed against the underside. The critical horizontal acceleration at which the normal reaction just becomes zero is:

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G1 Physics · Accepted Answer

At the limiting condition N = 0. Resolve gravity and pseudo force perpendicular to the plane. For the chosen acceleration direction, the pseudo-force normal component is ma sinθ and the gravitational normal component tending to separate the block is mg cosθ. At loss of contact, ma sinθ = mg cosθ. Therefore a = g cotθ.