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
B. `N_(BC)` increases
C. `N_(AB)` remains constant
D. `N_(BC)` remains constant

Answer

B, C

Explanation

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.