Question

A cylinder rests in a supporting carriage as shown. The side AB of carriage makes an angle ${30}^0$ 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(s).

• A. $N_{AB}$ increases
• B. $N_{BC}$ increases
• C. $N_{AB}$ remains constant
• D. $N_{BC}$ remains constant

Answer 1

Answer: (B), (C)

The correct options are
B $N_{AB}$ remains constant
C $N_{BC}$ increases

Answer is B and C.
From the FBD of cylinder we get,
$mg=N_{AB}\cos {30}^0$
$N_{AB}=\frac{2mg}{\sqrt{3}}$

Above equations show that $N_{AB}$ is independent of acceleration a and hence remains constant
Further,
$N_{BC}=ma+N_{AB}\cos {60}^0$
$N_{BC}=m(a+\frac{g}{\sqrt{3}})$
Hence $N_{BC}$ increases with increase in acceleration.