Question

A wooden block is placed on a rough horizontal surface. It is given a velocity \( u \) m/s and the coefficient of friction between the block and the surface is \( \mu \). The distance covered by the block before coming to rest is: (g = acceleration due to gravity)

• A. \( \frac{u^2}{\mu g} \)
• B. \( \frac{u^2}{2 \mu g} \)
• C. \( \frac{u}{\mu g} \)
• D. \( \frac{u}{\mu^2 g} \)

Hint:

The distance traveled by an object under friction can be found using the work-energy principle, where the work done by friction is equal to the change in kinetic energy.

Answer 1

The Correct Option is B

Step 1: Work-Energy Principle.
The block moves under the influence of friction, and the work done by the frictional force brings the block to rest. The frictional force is given by: \[ f = \mu mg \] where \( m \) is the mass of the block and \( g \) is the acceleration due to gravity. The work done by the frictional force is equal to the change in kinetic energy: \[ \text{Work} = f \times d = \mu mg \times d = \frac{1}{2} m u^2 \] where \( d \) is the distance covered by the block and \( u \) is the initial velocity. Solving for \( d \), we get: \[ d = \frac{u^2}{2 \mu g} \] Step 2: Final Answer.
Thus, the distance covered by the block before coming to rest is \( \frac{u^2}{2 \mu g} \).