Umakant Kondapure, Collin Fernandes, Nipun Bhatia, Vikram Bathula and, Ketki Deshpande Solutions for Chapter: Gravitation, Exercise 4: Evaluation Test

For a particle projected in a transverse direction from a height h above earth's surface, find the minimum initial velocity so that it grazes the surface of earth such that path of this particle would be an ellipse with centre of earth as the farther focus, point of projection as the apogee and a diametrically opposite point on earth as perigee.

A particle is dropped on Earth from height $R$ (radius of earth) and it bounces back to height $h$. If the coefficient of restitution of collision is $\sqrt{\frac{2}{3}},$ then find $h$.

A uniform spherical planet (radius $R$) has acceleration due to gravity at its surface as $g$. Points $P$ and $Q$ located inside and outside the planet, respectively have acceleration due to gravity $\frac{g}{4}$. Maximum possible separation between $P$ and $Q$ is

A comet is moving around the earth in highly elliptical orbit. Identify the incorrect statement.

Two particles are projected from the surface of the earth with velocities $\sqrt{\frac{5}{7}\mathrm{gR}}$ and $\sqrt{\frac{2}{5}\mathrm{gR}}$ where, $R$ is the radius of the earth. What would be the ratio of maximum heights attained?

A triple star consists of two stars, each of mass $m$ in the same circular orbit about a central star of mass $M=10\times {10}^{30} \mathrm{kg}.$ The two opposite stars always lie at opposite ends of a diameter. The radius of circular orbit is $r=2\times {10}^{11} \mathrm{m}$ and period is $0.6\times {10}^7 \mathrm{s}.$ Find $m. \left(\mathrm{in} \mathrm{kg}\right)$
$\left[\mathrm{Given} {\pi }^2=10, \mathrm{G}=\frac{20}{3}\times {10}^{-11} \mathrm{N} {\mathrm{m}}^2 {\mathrm{kg}}^{-2}\right]$

Consider a hypothetical planet which is very long and cylindrical. The density of planet is $\rho$ and radius is R.

What is the possible orbital speed of the satellite in moving around the planet?

If a satellite is travelling in the same direction as the rotation of earth, i.e., west to east, what is the interval between two successive times at which it will appear vertically overhead to an observer at a fixed point on the equator? $\left(R=6400 \mathrm{km}, h=1400 \mathrm{km}\right)$