NEET Physics Gravitation Escape Velocity MCQs

A planet has a radius R and density $\rho$. A satellite is launched from its surface with a speed $v = \sqrt{\frac{8}{9} \frac{4\pi G\rho R^2}{3}}$. The maximum height attained by the satellite above the planet's surface is:

Two planets A and B have identical radii but different densities, $\rho_A$ and $\rho_B$, respectively, where $\rho_A = 2\rho_B$. The ratio of their escape velocities, $v_A/v_B$, is:

A black hole has an escape velocity equal to the speed of light, c. If a planet of the same mass as the black hole had a radius R, what would be the radius of the black hole, assuming uniform density for both?

If the escape velocity at the surface of a planet is $v_e$, and a projectile is launched vertically with a speed of $\frac{v_e}{\sqrt{2}}$, the maximum height reached by the projectile above the surface is:

A spherical planet of uniform density $\rho$ and radius R has a tunnel drilled through its center. An object is dropped into the tunnel. The time it takes to reach the other side of the planet is:

A particle is projected from the surface of a non-rotating planet of radius R with escape velocity. Neglecting atmospheric resistance, which of the following best describes the path of the particle?

If the radius of Earth were to shrink to half its present value, with its mass remaining the same, what would happen to the escape velocity?

The escape velocity from a planet's surface is $v$. What would be the escape velocity of a satellite orbiting the planet at a height equal to its radius?

Which of the following factors does not affect the escape velocity of a planet?

Escape velocity is the minimum velocity required for an object to: