Question

A body of mass $10 kg$ is moving with an initial speed of $20 m / s$ The body stops after $5 s$ due to friction between body and the floor The value of the coefficient of friction is: (Take acceleration due to gravity $g =10 ms ^{-2}$ )

• A. $0.2$
• B. $0.4$
• C. $0.5$
• D. 0.3

Hint:

The coefficient of friction can be found by equating the work done by the frictional force to the change in kinetic energy of the body.

Answer 1

The Correct Option is B

To find the coefficient of friction, we need to analyze the forces acting on the body. The body has an initial speed of \(20 \, \text{m/s}\) and stops in \(5 \, \text{s}\) due to friction. Let's proceed step-by-step:

1. The initial velocity of the body, \(u = 20 \, \text{m/s}\).
2. The final velocity of the body when it stops, \(v = 0 \, \text{m/s}\).
3. The time duration over which the body comes to a stop, \(t = 5 \, \text{s}\).

We can calculate the acceleration using the first equation of motion:

\(v = u + at\)

Substituting the known values:

\(0 = 20 + a \times 5\)

Solving for \(a\) (acceleration), we get:

\(a = \frac{-20}{5} = -4 \, \text{m/s}^2\)

The negative sign indicates that the acceleration is acting in the direction opposite to the motion (deceleration).

1. The force of friction \((f)\) is given by:

\(f = \text{mass} \times \text{acceleration} = 10 \times (-4) = -40 \, \text{N}\)

1. The negative sign again indicates force opposing motion.
2. The frictional force can also be given by:

\(f = \mu \times m \times g\)

1. where \(\mu\) is the coefficient of friction, \(m\) is the mass and \(g\) is acceleration due to gravity, which is given as \(10 \, \text{m/s}^2\).

Substituting the known values into the equation for frictional force:

\(-40 = \mu \times 10 \times 10\)

Solving for \(\mu\):

\(\mu = \frac{-40}{100} = 0.4\)

Thus, the coefficient of friction is \(0.4\), which matches the correct answer option given.