Laws of MotionHard
Question
A cylinder rests in a supporting carriage as shown. The side AB of carriage makes an angle 30o 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:
Options
A.NAB increases and NBC decreases.
B.Both NAB and NBC increase.
C.NAB remains constant and NBC increases.
D.NAB increases and NBC remains constant.
Solution
The free body diagram of cylinder is as shown.
Since net acceleration of cylinder is horizontal,
NAB cos30o = mg or NAB =
mg .... (1) and NBC − NAB sin30o = ma or NBC = ma + NAB sin 30o .... (2)
Hence NAB remains constant and NBC increases with increase in a.
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