A thin horizontal circular disc is rotating about a vertical axis passing through its centre. An insect is at rest at a point near the rim of disc. The insect now moves along a diameter of the disc to reach its other end. During the journey of the insect, the angular speed of the disc
Three bodies having masses $$5 \mathrm{~kg}, 4 \mathrm{~kg}$$ and $$2 \mathrm{~kg}$$ is moving at the speed of $$5 \mathrm{~m} / \mathrm{s}, 4 \mathrm{~m} / \mathrm{s}$$ and $$2 \mathrm{~m} / \mathrm{s}$$ respectively along $$X$$-axis. The magnitude of velocity of centre of mass is
Two satellites $$A$$ and $$B$$ revolve round the same planet in coplanar circular orbits lying in the same plane. Their periods of revolutions are $$1 \mathrm{~h}$$ and $$8 \mathrm{~h}$$, respectively. The radius of the orbit of $$A$$ is $$10^4 \mathrm{~km}$$. The speed of $$B$$ is relative to $$A$$. When they are closed in $$\mathrm{km} / \mathrm{h}$$ is
A planet is revolving around the sun in a circular orbit with a radius $$r$$. The time period is $$T$$. If the force between the planet and star is proportional to $$r^{-3 / 2}$$, then the square of time period is proportional to