Question

A small ball of mass $m$ starts at a point $A$ with speed $v_0$ and moves along a frictionless track $AB$ as shown. The track $BC$ has the coefficient of friction $\mu$. The ball comes to stop at $C$ after travelling a distance $L$ which is

• A. $\frac{h}{2\mu }+\frac{v_0^2}{2\mu g}$
• B. $\frac{h}{\mu }+\frac{v_0^2}{2\mu g}$
• C. $\frac{2h}{\mu }+\frac{v_0^2}{2\mu g}$
• D. $\frac{h}{2\mu }+\frac{v_0^2}{\mu g}$

Answer 1

The correct option is B $\frac{h}{\mu }+\frac{v_0^2}{2\mu g}$

Given: a small ball of mass m starts at a point A with speed $v_0$ and moves along a frictionless track AB as shown. The track BC has the coefficient of friction $\mu$

To find the ball comes to stop at C after travelling a distance L

Solution:

Initial speed at point A, $u=v_0$

Speed point B, $V=?$

Therefore,

$V^2-u^2=2gh⟹V^2=v_0^2+2gh$

Let ball travels distance L before coming to rest, then

$L=\frac{V^2}{2\mu g}⟹L=\frac{v_0^2+2gh}{2\mu g}⟹L=\frac{v_0^2}{2\mu g}+\frac{h}{\mu }$

is the distance travelled by ball before coming to stop.