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A cylinder rests in a supporting carriag...

A cylinder rests in a supporting carriage as shown. The side AB of carroage makes an angle `30^(@)` with the horizontal and side BC is vertical. The carriage lies on a fixed 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 evergywhere. Then as the magnitude of acceleration 'a' of the carriage is increased pick up the correct statement(s) :

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

Text Solution

Verified by Experts

The correct Answer is:
A, B, D

The free body diagram of cylinder is as shown. Since net acceleration of cylinder is horizontal,
`N_(AB)cos30^(@)=mg` or `N_(AB)=(2)/(sqrt(3))mg` ..(1)
and `N_(BC)-N_(AB)=sin30^(@)=ma` or `N_(BC)=ma+N_(AB)sin30^(@)` ..(2)
Hence `N_(AB)` remains constant and `N_(BC)` increases with increases in a.
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