Let `F,F_N and f` denote the magnitudes of the contact force, normal force and the friction exerted by one surface on the other kept in contact. If none of these is zero,

Options

A. `F gt f`
B. `F_(N) gt f`
C. `F gt F_(N)`
D. `F_(N)-f lt f lt F_(N)+f`

Answer

A, C

Explanation

Hence `F=sqrt(f^(2)+F_(N)^(2))` Hence `F gt F_(N) & F gt f`
Also `F=sqrt(F_(N)^(2)+f^(2)+2F_(N)f-2F_(N)f)`
`=sqrt((F_(N)+f)^(2)-2F_(N)f)=(F_(N)+f)-delta`
Again `F=sqrt(F_(N)^(2)+f^(2)-2F_(N)f+2F_(N)f)`
`=sqrt((F_(N)-f)^(2)+2F_(N)f)=(F_(N)-f)+delta gt (F_(N)-f)`
Hence `F_(N)-f lt f lt F_(N)+f`