NEET Physics MCQs

Given the expression for the escape velocity $v_e = \sqrt{\frac{2GM}{R}}$, where $G$ is the gravitational constant, $M$ is mass, and $R$ is radius. If a new quantity $Y$ is defined as $Y = \frac{v_e^3}{\sqrt{GM}}$, what are the dimensions of $Y$?

Derive the expression for the escape velocity of an object from the surface of a planet of mass 'M' and radius 'R'.

A particle of mass 'm' moves under the influence of a central force given by $F(r) = -\frac{k}{r^3}$, where 'k' is a positive constant. If the particle's initial velocity is 'v' at a distance 'r' from the center of the force, what is the minimum velocity required for the particle to escape to infinity?

A particle is projected vertically upwards from the surface of Earth with a speed equal to half the escape velocity. The maximum height reached by the particle, measured from the surface of Earth, is (R = radius of Earth):

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?