A small block of mass m is kept on the inclined surface of a wedge of mass M. The inclined surface of the wedge makes an angle `theta` with the horizontal. The wedge is kept on a frictionless rigid horizontal floor. You can neglect friction between the block and the wedge also. An external agent applies a horizontal force F on the wedge.

The value of the force F so that the wedge remains at rest is `F_(1)`. Which of the options is incorrect?

Options

A. `F_(1)` is less than mg sin `theta`
B. `F_(1)` is less then mg cos `theta`
C. `F_(1)` does not depend on M
D. It is not possible to keep the wedge at rest

Answer

D

Explanation

`N = m g cos theta` and `F_(1) = N sin theta`
`implies F_(1) = m g sin theta cos theta`
`R = mg + N cos theta`
`= mg + mg cos^(2) theta`