A small block of mass m is kept on a rough inclined surface of inclination `theta` fixed in an elevator. The elevator goes up with a uniform velocity v and te block does not slide n te wedge. The work done by the force of friction on the block in time t will be

Options

A. zero
B. `mgvt cos^(2)theta`
C. `mgvt sin^(2)theta`
D. `(1)/(2)mgvt sin2theta`

Answer

C

Explanation

(c ) As block does not slide. Hence force of friction,

f=mg sin `theta`
In time t, displacement s=vt
`:. " " W_(f)=f.s.cos (90^(@)-theta)`
`=(mg sin theta)(vt)(sin theta)`
`=mgvt sin^(2) theta`