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 $N_{AB} and N_{BC}$ respectively. Neglect friction everywhere. Then as the magnitude of acceleration 'a' of the carriage is increased, pick up the correct statement:

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$N_{AB}$ increases and $N_{BC}$ decreases.

$Both N_{AB} and N_{BC} increase .$

$N_{AB} remains constant and N_{BC} increases .$

$N_{AB} increases and N_{BC} remains constant$

answer is C.

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Detailed Solution

The free body diagram of cylinder w.r.t. carriage is as shown.

Since net acceleration of cylinder is horizontal,

$N_{AB} \cos 30 ° = mg$

or $N_{AB} = \frac{2}{\sqrt{3}} mg$ ------------(1)

$and N_{BC} = ma + N_{AB} \sin 30^{0} - - - - - - (2)$

Hence $N_{AB}$ remains constant and $N_{BC}$ increases with increase in a.

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