Question

A body is travelling with $ 10\, \text{m/s} $ on a rough horizontal surface. Its velocity after $ 2\, \text{s} $ is $ 4\, \text{m/s} $. The coefficient of kinetic friction between the block and the plane is
(acceleration due to gravity = $ 10\, \text{m/s}^2 $)

• A. 0.4
• B. 0.3
• C. 0.5
• D. 0.2

Hint:

Use the kinematic equation \( v = u + at \) to find acceleration, then relate it to friction using \( f = \mu mg \).

Answer 1

The Correct Option is B

We are given: - Initial velocity \( u = 10\, \text{m/s} \)
- Final velocity \( v = 4\, \text{m/s} \)
- Time \( t = 2\, \text{s} \)
We can use the first equation of motion: \[ v = u + at \Rightarrow 4 = 10 + a \cdot 2 \Rightarrow a = \frac{4 - 10}{2} = -3\, \text{m/s}^2 \] The retardation is due to kinetic friction. For a horizontal surface: \[ f_k = \mu_k mg \Rightarrow ma = -\mu_k mg \] Dividing both sides by \( m \): \[ a = -\mu_k g \Rightarrow \mu_k = -\frac{a}{g} = \frac{3}{10} = 0.3 \]