Question

A metal ball of mass m is put at the point A of a loop track and the vertical distance of A from the lower most point of track is 8 times the radius R of the circular part. The linear velocity of ball when it rolls of the point B to a height R in the circular track will be

• A. $[10gR{]}^{\frac{1}{2}}$
• B. $7{\left[\frac{gR}{10}\right]}^{\frac{1}{2}}$
• C. $7{\left[\frac{7gR}{5}\right]}^{\frac{1}{2}}$
• D. $[5gR{]}^{\frac{1}{2}}$

Answer 1

The correct option is A

$[10gR{]}^{\frac{1}{2}}$

Conservation of energy principle gives us,

$8mgR=\frac{1}{2}m{v}^2+\frac{1}{2}\left(\frac{2}{5}m{R}^2\right){\left(\frac{v}{R}\right)}^2+mgR$

$\Rightarrow V=\sqrt{10gR}$