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A cylinder rests in a supporting carriag...

A cylinder rests in a supporting carriage as shown. The side AB of carriage makes an angle `30^(@)` with the horizontal and side BC is vertical. The carriage lies on a fixed horizontal surface and is being puplled towards left with an horizontal acceleration `a` . The magnitude of normal reactions exerted by side AB and BC of carriage on the cylinder be `N_(AB)` and `N_(BC)`resectively. Neglect friction everywhere. Then as the magnnitude of acceleration `a` of the carriage is increased, pick up the correct statement:

A

`N_(AB)` increases

B

`N_(BC)` increases

C

`N_(AB)` remains constant

D

`N_(BC)` remains constant

Text Solution

Verified by Experts

The correct Answer is:
B, C

The free body diagram of cylinder is as shown
Since net acceleration of cylinder is horizontal
`N_(AB) cos 30^(@) = mg`
or `N_(AB) = (2)/(sqrt(3))mg`....(1)
and `N_(BC) = N_(AB) sin 30^(@) = ma`
or `N_(BC) = ma + N_(AB) sin 30^(@)` ....(2)
Hence `N_(AB)` remains constant and `N_(BC)` increases will increase in a.
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