Exams › JEE Main › Physics

Two spherical stars A and B have densities rho_A and rho_B. They start with the same radius, and their masses satisfy M_B = 2*M_A. In an interaction, star A loses mass so that its radius becomes half its original value while staying spherical and keeping its density rho_A. All the mass shed by A is added onto B as a thick uniform spherical shell of density rho_A. Let v_A and v_B be the escape speeds from A and B after this process. If v_B/v_A = sqrt(10n / 15^(1/3)), find the value of n.

1. 2.3
2. 1.5
3. 4.6
4. 3.0

Correct answer: 2.3

Solution

Track masses and radii after the redistribution, then use the escape-velocity formula. The new radius of B comes from adding the shed volume (mass/density rho_A) to B's original volume.

Related JEE Main Physics questions

• A satellite of mass m moves in a circular orbit around the Earth at an altitude x above the Earth's surface. If g denotes the acceleration due to gravity at the Earth's surface, then the satellite's orbital speed is
• A particle is launched vertically upward from Earth’s surface with speed equal to three-fourths of the escape speed. The maximum distance of the particle from the Earth’s center is (take Earth’s radius as R):
• If Earth’s radius became 1% smaller while its mass stayed unchanged, what would happen to the acceleration due to gravity at the surface?
• The Moon takes about 29 days to complete one revolution around the Earth. If the Moon’s mass were doubled while every other factor stayed the same, its orbital period would be approximately
• Let the Earth have mean radius R, angular velocity ω about its own axis, and surface gravitational acceleration g. The orbital radius of a geostationary satellite is:
• Assume the Earth is a uniform sphere. Scientist A descends into a mine, while scientist B rises in a balloon. As they move, the gravitational field experienced by A keeps decreasing and the field experienced by B also keeps decreasing. Which statement best describes their rates of decrease?

⚔️ Practice JEE Main Physics free + battle 1v1 →