Question

A cylinder rests in a supporting carriage as shown. The side AB of carriage makes an angle ${30}^{\circ }$ with the horizontal and side BC is vertical. The carriage lies on a fixed horizontal surface and is being pulled towards left with a horizontal acceleration ‘a’. The magnitude of normal reactions exerted by sides AB and BC of carriage on the cylinder be $N_{AB}\text{and}{N}_{BC}$respectively. Neglect friction everywhere. Then as the magnitude of acceleration ‘a’ of the carriage is increased, choose the correct statement:

• A. N_AB increases and N_BC decreases
• B. Both N_AB and N_BC increase
• C. N_AB remains constant and N_BC increases
• D. N_AB increases and N_BC remains constant

Answer 1

The correct option is C

N_AB remains constant and N_BC increases

The free body diagram of cylinder is as shown.

Since net acceleration of cylinder is horizontal,

$N_{AB}cos{30}^0=mgor{N}_{AB}-\frac{2}{\sqrt{3}}mg\cdots \left(1\right)\text{And}{N}_{BC}-N_{AB}sin{30}^0=maor{N}_{BC}=ma+N_{AB}sin{30}^0\cdots \left(2\right)$

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