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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 and `N_(BC)` decreses.

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:
C

The free body diagram of cylinder w.r.t carriage is as shown. Since net acceleration of cylinder is horizontal,
`N_(AB)cos30^@=mg`
or `N_(AB)=(2)/(sqrt(3))mg`
F.B.D of cylinder w.r.t to carriage
and `N_(BC)=ma+N_(AB)sin30^@`
Hence `N_(AB)` remains constant and `N_(BC)` increases with increase in a.
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