Question

A thin hollow cylinder open at both ends: (I) sliding without rolling (II) Rolls without slipping, with the same speed. The ratio of kinetic energy in the two cases is?

• A. $1:1$
• B. $4:1$
• C. $1:2$
• D. $2:1$

Answer 1

The correct option is A $1:1$

For Case I :

$\Rightarrow K.E_1=\frac{1}{2}m{v}^2⟶\left(1\right)$

For Case II :

$\Rightarrow K.E_2=\frac{1}{2}I{w}^2$

$=\frac{1}{2}\times m{R}^2\times \frac{v^2}{R^2}=\frac{1}{2}m{v}^2⟶\left(2\right)$

$\therefore K.E_1:K.E_2=1:1.$

Hence, the answer is $1:1.$