A particle of mass $m$ moves around the origin in a potential $\frac{1}{2} m \omega^{2} r^{2}$, where $r$ is the distance from the origin. Applying the Bohr's model in this case, the radius of the particle in its $n$th orbit in terms of $a=\sqrt{h /(2 \pi m \omega)}$ is

Two bodies of masses ${m_1}$ and ${m_2}$ are initially at rest at infinite distance apart. They are then allowed to move towards each other under mutual gravitational attraction. Their relative velocity of approach at a separation distance $r$ between them is

How much energy will be necessary for making a body of 500 kg escape from the earth $[g = 9.8\,m/{s^2}$, radius of earth $ = 6.4 \times {10^6}\,m]$

If radius of an orbiting satellite is decreased, then its kinetic energy

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