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Question

# A cylinder rests in a supporting carriage as shown. The side AB of carriage makes an angle 30∘ with the horizontal and side BC is vertical. The carriage lies on a fixed horizontal surface and is being pulled towards left with an horizontal acceleration ′a′. The magnitude of normal reactions exerted by sides AB and BC of carriage on the cylinder be NAB and NBC respectively. Neglect friction everywhere. Then as the magnitude of acceleration ′a′ of the carriage is increased, pick up the correct statement.

A
NAB increases and NBC decreases.
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B
Both NAB and NBC increase
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C
NAB remains constant and NBC increases
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D
NAB increases and NBC remains constant
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Solution

## The correct option is C NAB remains constant and NBC increasesFBD of the sphere (rest frame of the carriage) For equilibrium, Along y− axis, NAB cos 30∘=mg NAB=2 mg√3 (constant) Along x− axis, NBC=ma+NAB sin 30∘ NBC=ma+mg√3 ⇒ as ′a′ increases, NBC increases.

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