Embibe Experts Solutions for Chapter: Gravitation, Exercise 1: Exercise#1

Two particles, each of mass $M$, move around in a circle of radius $R$ under the action of their mutual gravitational attraction. The speed of each particle is,

With what angular velocity should the earth spin so that a body lying at $37°$ latitude becomes weightless?

Which of the following graphs represent the time period of the planet moving around the sun? [$R$ is semi-major axis of the path.]

The orbital velocity of an artificial satellite in a circular orbit just above the earth's surface is $V_0$. The value of orbital velocity for another satellite orbiting at an altitude of half of earth's radius is,

If the distance between the earth and the sun were half its present value, then the number of days in a year would have been,

A satellite is launched into a circular orbit of radius $R$ around the earth. A second satellite is launched into an orbit of radius $1.02R$. The period of second satellite is larger than the first one by approximately,

A satellite is moved from one circular orbit around the earth to another one of the lesser radius. Which of the following statements is true?

The mass of a spaceship is $1000 \mathrm{kg}$. It is to be launched from the earth's centre out into free space. The value of $g$ and $R$ (radius of earth) are $10 \mathrm{m} {\mathrm{s}}^{-2}$ and $6400 \mathrm{km}$, respectively. The required energy for this work will be,