Question

A block of mass m is placed on a rough Inclined plane of inclination $\theta$ kept on the floor of the lift. the elevator goes up with a uniform velocity v and the bloc does not slide on the wedge. the work was done by the force of friction on the block in the time T will be?

• A. Zero
• B. $mgvtcos2\theta$
• C. $mgvtsi{n}^2\theta$
• D. None of the above

Answer 1

The correct option is C $mgvtsi{n}^2\theta$

Displacement of block in time 't' $=vt$

As block does not slide so

Force of friction =$\mu mgsin\theta$

Angle between force and displacement is $90-\theta$

Work done= $force\times displacement$

=$mgsin\theta \times vt\times cos(90-\theta )$

=$mgvtsi{n}^2\theta$