If g is the acceleration due to gravity at the earth's surface and r is the radius of the earth,

step 1 Hello students in this question we have a body of mass small m which is at rest at a distance ca

If g is the acceleration due to gravity at the earth's...

If $\mathrm{g}$ is the acceleration due to gravity at the earth's surface and $\mathrm{r}$ is the radius of the earth, the escape velocity for the body to escape out of earth's gravitational field is $\ldots \ldots \ldots$ (A) $\mathrm{gr}$ (B) $\sqrt{(2 \mathrm{gr})}$ (C) $\mathrm{g} / \mathrm{r}$ (D) $\mathrm{r} / \mathrm{g}$

If $\mathrm{g}$ is the acceleration due to gravity at the earth's surface and $\mathrm{r}$ is the radius of the earth, the escape velocity for the body to escape out of earth's gravitational field is $\ldots \ldots \ldots$
(A) $\mathrm{gr}$
(B) $\sqrt{(2 \mathrm{gr})}$
(C) $\mathrm{g} / \mathrm{r}$
(D) $\mathrm{r} / \mathrm{g}$

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Key Concepts

Conservation of Energy

The conservation of energy principle states that energy cannot be created or destroyed, only transformed from one form to another. In the context of escape velocity, this principle is applied by equating the kinetic energy of an object with the energy required to overcome the gravitational potential energy, providing the basis for deriving the escape velocity formula.

Gravitational Potential Energy

Gravitational potential energy is the energy held by an object due to its position in a gravitational field. It plays a crucial role in understanding escape conditions because an object must have enough kinetic energy to overcome the gravitational potential energy that is holding it in place.

Escape Velocity

Escape velocity is the minimum speed required for an object to break free from the gravitational pull of a celestial body without further propulsion. It is derived by equating the kinetic energy of the moving object to the gravitational potential energy that binds it to the body, thereby ensuring that the object can reach an infinite distance where the gravitational influence becomes negligible.

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