NEET Questions

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:

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 satellite is in a circular orbit around Earth. If its orbital radius is doubled, how does its orbital speed change?

Two satellites, A and B, are orbiting a planet at different altitudes. Satellite A has a period $T_A$ and an orbital radius $r_A$. Satellite B has an orbital radius $r_B = 4r_A$. Assuming the planet's mass is much greater than the satellites' masses, what is the period of satellite B, $T_B$?

A satellite is in a circular orbit around a planet. If its kinetic energy is doubled, and assuming no external forces act on it, what will happen to its orbital radius?

Consider a binary star system where two stars of equal mass $M$ orbit each other in circular orbits of radius $R$. What is the orbital speed of each star?

A binary star system consists of two stars of masses $M$ and $2M$ separated by a distance $d$. A small asteroid of mass $m$ is placed on the line joining the two stars at a distance $x$ from the star of mass $M$. If the net gravitational force on the asteroid is zero, the gravitational potential energy of the asteroid is:

A particle is projected vertically upwards from the surface of Earth with a velocity equal to half the escape velocity. Neglecting air resistance, what fraction of its initial kinetic energy will be its gravitational potential energy at the highest point?

Two spherical shells of masses $M$ and $2M$ and radii $R$ and $2R$ respectively are placed with their centres separated by a distance $5R$. A particle of mass $m$ is placed initially at the centre of the smaller shell. The minimum work required to move the particle to the centre of the larger shell is:

A satellite is orbiting Earth in a circular orbit of radius $R$. Its gravitational potential energy is $U$. If its orbital radius is doubled, its new gravitational potential energy will be: