Question

A ring of mass m and radius R has three particle attached to the ring as shown in the figure. The centre of the ring has a speed v₀. The kinetic energy of the system is (slipping is absent).

• A. $6 \text{m} \text{v}_{0}^{2}$
• B. $12 \text{m} \text{v}_{0}^{2}$
• C. $4 \text{m} \text{v}_{0}^{2}$
• D. $8 \text{m} \text{v}_{0}^{2}$

Answer 1

Answer: (A)

$\text{KE} = \frac{1}{2} \text{m} \left(\text{v}_{0}^{2}\right) + \frac{1}{2} \left(\text{mR}\right)^{2}\right) \left( \left(\frac{\left(\text{v}\right)_{0}}{\text{R}}\right)^{2}$
$= \frac{1}{2} \left(3 \text{m}\right) \left( \left(\sqrt{2} \left(\text{v}\right)_{0}\right)^{2} + \frac{1}{2} \left(\text{m}\right) \left( \left(2 \left(\text{v}\right)_{0}\right)^{2}$
$= 6 \text{m} \text{v}_{0}^{2}$