A small object is kept on a groove on rough incline plane of inclination `theta`. Groove wakes an angle `alpha` as shown in diagram. `mu` coefficient of friction. Which of the following is correct

Options

A. Normal force by incline plane. `N=mg cos theta`
B. Normal force by incline is `N=mgsqrt(cos^(2)theta+sin^(2)theta sin^(2) alpha)`
C. maximum frictional force that can develop is `f_(max)=mumg cos theta`
D. If `mu=0` then acceleration of blocks is `g sin theta cos alpha`

Answer

B, D

Explanation

`N_(1)= mg cos theta` perpendicular to the plane
`N_(2)= mg sin theta sin alpha`
`N_(2)` is in the plane of incline perpendicular to groove.
`N=sqrt(N_(1)^(2)+N_(2)^(2))` If `mu=0`
Net force along groove. `mg sin theta cos alpha`. Hence acceleration is `g sin theta cos alpha`.