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:

Options

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

Answer

A, B, D

Explanation

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.