Three blocks are placed at rest on a smooth inclined plane with force acting on `m_(1)` parallel to the inclined plane. Find the contact force between `m_(2)` and `m_(3)`

Options

A. `((m_(1)+m_(2)+m_(3))F)/(m_(3))`
B. `(m_(3)F)/(m_(1)+m_(2)+m_(3))`
C. `F-(m_(1)+m_(2))g`
D. None of the above

Answer

B

Explanation

(b) Acceleration of system, `a=(" Net pushing force")/(" Total mass")`
or `a=(F-(m_(1)+m_(2)+m_(3))g sin theta)/((m_(1)+m_(2)+m_(3)))`
Equation of motion for `m_(3)`
`N-m_(3)g sin theta=m_(3)a`
or `N=m_(3)g sin theta +m_(3)[(F-(m_(1)+m_(2)+(m_(3))/((m_(1)+m_(2)+m_(3)))]`
`=(m_(3)F)/(m_(1)+m_(2)+m_(3))`