A block of mass `m` rests on a fixed incline plane of inclination `theta` with horizontal Assume friction is large enough to make the block stationary. Then choose correct alternative (s)

Options

A. Maximum value of horizontal component of friction is mg
B. angle `theta` at which horizontal component of friction is maximum is `(pi)/(4)`
C. Maximum value of horizontal component of friction is `(mg)/(2)`
D. Angle `theta` at which horizontal component of friction is maximum is `(pi)/(3)`

Answer

B, C

Explanation

`f_(x)=mgsintheta`
`f_(x)=fcostheta=mgsinthetacostheta`
`f_(x)=(mg)/(2)(2theta)`
`f_(xmax)=(mg)/(2)`
`(theta=(pi)/(4))`