Escape Velocity

Write a short note on escape velocity.

The total energy of a body at an infinite distance from the earth's surface is equal to 

What is the value of gravitational potential energy of an object at infinite distance from the earth surface.

Find the escape velocity of a body from the earth. [R (earth) = $6.4\times {10}^6 \mathrm{m}$, $\rho$(earth) = $5.52\times {10}^3 {\mathrm{kgm}}^{-3}$, G = $6.67\times {10}^{-11} {\mathrm{Nm}}^2{\mathrm{kg}}^{-2}$]
 

The escape velocity of an object from the earth depends upon the mass of earth (M), its mean density ($\rho$), its radius (R), and gravitational constant (G), thus the formula for escape velocity is:

The escape velocity of a body from the earth’s surface, based on the principle of conservation of energy $V_{esc}$ is = _____ .
 

Find the escape velocity of a body from the earth. [M(earth) = $6\times {10}^{24} \mathrm{kg}$, R (earth) = $6.4\times {10}^6 \mathrm{m}$, G$=6.67\times {10}^{-11} {\mathrm{Nm}}^2{\mathrm{kg}}^{-2}$ ]

Using the law of conservation of energy, obtain the expression for the escape velocity.

The value of gravitational potential energy at an infinite distance from the earth is 

What is the kinetic energy of an object when it is at infinite distance from the earth?
 

If a missile launched with a velocity less than escape velocity, the sum of its $K.E$. and $P.E$. is always

A $U-$shaped smooth wire has a semi-circular bend of radius $R$ between $A$ and $B$. It is held fixed in a vertical plane. A bead of mass $m$ is released from height $h$ (above $A$) and slides smoothly along the wire to reach the same height on other side of the wire. It is given that $h\gg R$.

Consider the motion of the bead between $A$ and the lowest point $C$ of the wire. The ratio of change in magnitude of velocity of the particle at $A$ to the magnitude of change in its velocity at $C$ is nearly equal to