Question

A block of mass $M$ is pulled along a horizontal surface by applying a force at an angle $\theta$ with the horizontal. The friction coefficient between the block and the surface is $\mu$. If the block travels at a uniform velocity, the work done by this applied force during a displacement $d$ of the block is

• A. $\frac{\mu Mgd\cos \theta }{\cos \theta +\mu \sin \theta }$
• B. $\frac{\mu Mgd}{\cos \theta }$
• C. $\frac{\mu Mgd\sin \theta }{\cos \theta +\mu \sin \theta }$
• D. $\frac{\mu Mgd\cos \theta }{\sin \theta }$

Answer 1

The correct option is A $\frac{\mu Mgd\cos \theta }{\cos \theta +\mu \sin \theta }$

Let the applied force be F.

As the force F makes an angle x with the horizontal, so the component of the force in the horizontal direction is Fcosx.

This force tends to move the block inn the forward direction.

The other force that is acting on the block is the frictional force which acts opposite to the applied force.