NEET Physics Gravitation MCQs

A perfectly spherical planet X has twice the radius of Earth and half the average density. An object weighs 100 N on Earth's surface. What would be its weight on the surface of planet X?

Imagine a planet with a non-uniform density distribution. Its core has a density $\rho_c$, and the outer shell has a density $\rho_s$. If the core radius is half the total radius R, what core density $\rho_c$ would result in the same surface gravity as Earth (assuming the shell density $\rho_s$ is negligible)?

If Earth's density were doubled while its radius remained constant, the acceleration due to gravity at its surface would:

If Earth's radius were doubled while its mass remained constant, the acceleration due to gravity at its surface would:

A planet has a radius R and density $\rho$. If both are doubled, the acceleration due to gravity at its surface will:

At what height above the Earth's surface is the acceleration due to gravity half of its value at the surface? (R is the radius of Earth)

Two planets P1 and P2 orbit a star S in elliptical orbits with semi-major axes a1 and a2 respectively, where a1 > a2. If T1 and T2 are their respective periods, and at some point both planets are simultaneously at their respective aphelia, after how many periods of P1 will they simultaneously be at their respective aphelia again?

A satellite is in a low, circular orbit around Earth. A small, impulsive retro-rocket burn is executed, reducing the satellite's speed by a small amount $\Delta v$. Which of the following best describes the resulting orbit immediately after the burn?

A planet orbits a star in an elliptical orbit. At its perihelion, the planet's speed is $v_p$ and its distance from the star is $r_p$. At its aphelion, the planet's speed is $v_a$ and its distance from the star is $r_a$. Which of the following expressions correctly relates these quantities?

Two asteroids, A and B, orbit the Sun with periods $T_A$ and $T_B$ respectively, where $T_A = 2T_B$. Let $a_A$ and $a_B$ be their respective semi-major axes. If asteroid A has an orbital eccentricity of 0.2, what is the maximum possible eccentricity of asteroid B?