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# A cylinder rests in a supporting carriage as shown. The side AB of carriage makes an angle 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 respectively. Neglect friction everywhere. Then as the magnitude of acceleration 'a ' of the carriage is increased, pick up the correct statement:

- increases and decreases
- Both and increase
- remains constant and increases
- increases and remains constant

## The correct answer is: remains constant and increases

### The free body diagram of cylinder is as shown. Since net acceleration of cylinder is horizontal

and N_{BC} – N_{AB} sin30° = ma or N_{BC} = ma + N_{AB} sin 30° .... (2)

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

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