Teaching JKPSC Lecturership Mock Test Series 2024-25 Physical Sciences Classical Mechanics Rigid Body Dynamics
A stick of length l and mass M , initially upright on a frictionless table, starts falling under the influence of gravity. Using energy conservation, what is the expression for the speed ( \(\dot{y} \) ) of the center of mass as a function of the angle \(\theta\) from the vertical?
1
\(\dot{y} = \sqrt{\frac{6g \sin^2 \theta}{3 \sin^2 \theta + 1}} \)
2
\(\dot{y} = \frac{l}{2} \sin \theta \dot{\theta}\)
3
\(\dot{y}^2 = \frac{2 g y}{[1 + (1/3) \sin^2 \theta]}\)
4
\( \dot{y} = \sqrt{\frac{3 l g (1 - \cos \theta) \sin^2 \theta}{3 \sin^2 \theta + 1}} \)S