JEE Main · 2024 · 30 Jan 2024 · Shift 1 · Gravitation

The escape velocity from a spherical planet A is 10 km/s. The escape velocity from another planet B whose density and radius are 10% of those of planet A, is ______ m/s.

Net gravitational force at the centre of a square is found to be $F_1$ when four particles having mass $M,2M,3M$ and $4M$ are placed at the four corners of the square as shown in figure and it is $F_2$ when the positions of $3M$ and $4M$ are interchanged. The ratio …

Given below are two statements:
Statement I: A satellite is moving around earth in the orbit very close to the earth surface. The time period of revolution of satellite depends upon the density of earth.
Statement II: The time period of revolution of the satellite is …

Three masses 200 kg, 300 kg and 400 kg are placed at the vertices of an equilateral triangle with sides 20 m. They are rearranged on the vertices of a bigger triangle of side 25 m and with the same centre. The work done in this process ______ J.
(Gravitational constant …

Initially a satellite of 100 kg is in a circular orbit of radius $1.5{\mathrm{R}}_{\mathrm{E}}$. This satellite can be moved to a circular orbit of radius $3{\mathrm{R}}_{\mathrm{E}}$ by supplying $\alpha \times 10^6\mathrm{J}$ of energy. The value of $\alpha$ is ______.
(Take …

If a body of mass 1 kg falls on the earth from infinity, it attains velocity (v) and kinetic energy (k) on reaching the surface of earth. The values of v and k respectively are ____.
(Take radius of earth to be 6400 km and $\mathrm{g}=9.8\mathrm{m}/{\mathrm{s}}^2$)