WBJEE · Physics · Rotational Motion
A uniform rod AB of length 1m and mass 4kg is sliding along two mutually perpendicular frictionless walls OX and OY.
The velocity of the two ends of the rod A and B are 3 m/s and 4 m/s respectively, as shown in the figure. Then which
of the following statement(s) is/are correct?
- A The velocity of the centre of mass of the rod is 2.5 m/s.
- B Rotational kinetic energy of the rod is \(\frac{25}{6}\) joule.
- C The angular velocity of the rod is 5 rad/s clockwise.
- D The angular velocity of the rod is 5 rad/s anticlockwise.
Answer & Solution
Correct Answer
(D) The angular velocity of the rod is 5 rad/s anticlockwise.
Step-by-step Solution
Detailed explanation
Get \(\theta\) \[ 3 \cos \theta=4 \sin \theta \] \[ \begin{aligned} & \omega=\frac{3 \sin \theta+4 \sin \theta}{\ell} \\ & (\mathrm{KE})_{\text {rotation }}=\frac{1}{2} \frac{1}{12} \mathrm{ml}^2 \omega^2=\frac{25}{6} \end{aligned} \]
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