Question

A block of mass $M$ at the end of the string is whirled round a vertical circle of radius $R$. The critical speed of the block at the top of the swing is

• A. ${\left(R/g\right)}^{1/2}$
• B. $g/R$
• C. $M/Rg$
• D. ${\left(Rg\right)}^{1/2}$

Answer 1

Answer: (D)

${\left(Rg\right)}^{1/2}$

Using conservation of energy

Total mechanical energy at lowest point = Total mechanical energy at top

$\frac{1}{2}m{v}_{lowest}^2=\frac{1}{2}m{v}_{High}^2+2mgR$

we know that $v_{lowest}=\sqrt{5Rg}$

$\therefore \frac{1}{2}\left(5Rg\right)=\frac{1}{2}{v}_{high}^2+2gR$

$v_{high}=\sqrt{Rg}$