Question

In the track shown in figure section $AB$ is a quadrant of a circle of $1$ metre radius. A block is released at $A$ and slides without friction until it reaches $B$. After $B$ it moves on a rough horizontal floor and comes to rest at distance $3$ metres from $B$. What is the coefficient of friction between floor and body?

• A. $1/3$
• B. $2/3$
• C. $1/4$
• D. $3/8$

Answer 1

The correct option is A $1/3$

Let velocity at $B$ is $v_B$,

Using conservation of energy.

$\Rightarrow \frac{1}{2}m{v}_B^2=mgh$ $\Rightarrow v_B=\sqrt{20}$

Let retardation is $a$ provided by friction. $\Rightarrow a=\mu g$

Using $v^2=u^2-2as$

$\Rightarrow 0=20-2\times a\times 3$ $\Rightarrow a=\frac{10}{3}$

$\Rightarrow a=\mu g=\frac{10}{3}$ $\Rightarrow \mu =\frac{1}{3}$