Question

A stone of mass $10kg$ tied with a string of length $0.5m$ is rotated in a vertical circle. Find the total energy of the stone at the highest position. (in $J$)

• A. $123.36$
• B. $122.5$
  
• C. $154.3$
  
• D. $185.6$
  

Answer 1

The correct option is B $122.5$

assume that potential energy at lowest point is zero and stone is rotating with critical velocity

so the magnitude of velocity at highest point is $v=\sqrt{gl}$ where $l=$length of string

total energy $E=K.E.+P.E.$

$\Rightarrow K.E.=\frac{1}{2}m{v}^2=\frac{1}{2}10\times {\left(\sqrt{9.8\times 0.5}\right)}^2=24.5J$

$P.E.=mgh=mg\left(2l\right)=10\times 9.8\times (2\times 0.5)=98J$

so the total energy $E=98+24.5=122.5J$