Question

A marble block of mass $2kg$ lying on ice when given a velocity of $6m/s$ is stopped by friction in $10s$. Then, the coefficient of friction is

• A. $0.02$
• B. $0.03$
• C. $0.06$
• D. $0.01$

Answer 1

The correct option is C

$0.06$

Step 1. Given data:

Mass of marble block, $m=2kg$

Velocity, $v=6m{s}^{-1}$

Stopping time,$t=10s$

Frictional force, $f$

Step 2. Calculating back acceleration/Retardation:

Retardation, $a=\frac{v}{t}$

$\Rightarrow a=\frac{6}{10}$

Therefore, $a=0.6m/s^2$

Step 3. Balancing forces on the marble block

$\sum _{}^{}F=ma$

$f=ma$ $\left[f=\mu mg\right]$

$$\begin{gathered} \Rightarrow \mu mg=ma \\ \Rightarrow \mu =\frac{a}{g} \\ \Rightarrow \mu =\frac{0.6}{10} \\ \therefore \mu =0.06 \end{gathered}$$

Hence, option (C) is correct.