Q130 / 160 · AP EAMCET 2024 (22 May Shift 2) · Physics

A ring and a disc of same mass and same diameter are rolling without slipping. Their linear velocities are same, then the ratio of their kinetic energy is

  • A
    0.75
  • Correct answer
    B
    1.33
  • C
    0.5
  • D
    2.66

Solution

For ring, $\frac{\mathrm{K}^2}{\mathrm{R}^2}=1$ For disc, $\frac{\mathrm{K}^2}{\mathrm{R}^2}=\frac{1}{2}$ $\begin{aligned} & \frac{(\mathrm{K} . \mathrm{E})_{\text {ring }}}{(\mathrm{K} . \mathrm{E})_{\text {disc }}}=\frac{\left[\frac{1}{2} \mathrm{mv}^2\left(1+\frac{\mathrm{K}^2}{\mathrm{R}^2}\right)\right]_{\text {ring }}}{\left[\frac{1}{2} \mathrm{mv}^2\left(1+\frac{\mathrm{K}^2}{\mathrm{R}^2}\right)\right]_{\text {disc }}} \\ & =\frac{(1+1)}{\left(1+\frac{1}{2}\right)}=\frac{2 \times 2}{3}=1.33 \end{aligned}$

Hence, the correct answer is option: 'B'.

Relevant Questions