JEE Advanced · Physics · 8. Rotational Motion
Paragraph :
\(\mathbf{P}_{17 \text { - } 19}\) : Paragraph for Questions Nos. 17 to 19 Two discs \(A\) and \(B\) are mounted coaxially on a vertical axle. The discs have moments of inertia I and 2I, respectively about the common axis. Disc \(A\) is imparted an initial angular velocity \(2 \omega\) using the entire potential energy of a spring compressed by a distance \(x_1\). Disc \(B\) is imparted an angular velocity \(\omega\) by a spring having the same spring constant and compressed by a distance \(x_2\). Both the discs rotate in the clockwise direction.
Question :
The loss of kinetic energy during the above process is
- A \(\frac{I \omega^2}{2}\)
- B \(\frac{i \omega^2}{3}\)
- C \(\frac{I \omega^2}{4}\)
- D \(\frac{I \omega^2}{6}\)
Answer & Solution
Correct Answer
(B) \(\frac{i \omega^2}{3}\)
Step-by-step Solution
Detailed explanation
Loss of kinetic energy \(=K_i-K_f\)
\(
\begin{aligned}
& =\left\{\frac{1}{2} I(2 \omega)^2+\frac{1}{2}(2 I)(\omega)^2\right\}-\frac{1}{2}(3 I)\left(\frac{4}{3} \omega\right)^2 \\
& =\frac{1}{3} I \omega^2
\end{aligned}
\)
\(\therefore\) Option (b) is correct.
\(
\begin{aligned}
& =\left\{\frac{1}{2} I(2 \omega)^2+\frac{1}{2}(2 I)(\omega)^2\right\}-\frac{1}{2}(3 I)\left(\frac{4}{3} \omega\right)^2 \\
& =\frac{1}{3} I \omega^2
\end{aligned}
\)
\(\therefore\) Option (b) is correct.
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