A block of mass 20 kg slides on a rough horizontal plane surface. Let the speed of the block at a particular instant is 10 m/s. It comes to rest after travelling a distance of 20 m. Which one of the following could be the magnitude of the frictional force?

Solution:

The block comes to rest after traveling a distance of 20 m. We can use the work-energy principle to find the frictional force. The work done by the frictional force is equal to the change in kinetic energy of the block.

The initial kinetic energy (K.E.) of the block is given by:

K.E. = (1/2) × m × v² = (1/2) × 20 × (10)² = 1000 J

The work done by the frictional force is:

W = F × d

Where F is the frictional force and d is the distance traveled (20 m). Since the block comes to rest, all the kinetic energy is used up by the frictional force. Therefore:

1000 J = F × 20

Solving for F:

F = 1000 / 20 = 50 N

Hence, the magnitude of the frictional force is 50 N (Option 4).