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 madnnitude of acceleration `a` of the carriage is increased, pick up the correct statement:

Options

A. `N_(AB)` increases and `N_(BC)` decreases.
B. Both `N_(AB)` and `N_(BC)` increases..
C. `N_(AB)` remains constant and `N_(BC)` increases.
D. `N_(AB)` increases and `N_(BC)` remains contant.

Answer

C

Explanation

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` (1)
F.B.D of cylinder w.r.t. to carriage
and `N_(BC)=ma+N_(AB)sin30^(@)` (2)
Hence `N_(BC)` remains constant and `N_(BC)` increases with increases in `a` .