Imagine a new planet having the same density as that of the Earth but 3 times bigger than the Earth in size. If the acceleration due to gravity on the surface of the earth is g and that on the surface of the new planet is g', then:
1. | g' = 3g | 2. | g' = 9g |
3. | g' = g/9 | 4. | g' = 27g |
For a planet having mass equal to the mass of the earth but radius equal to one-fourth of the radius of the earth, its escape velocity will be:
1. | 11.2 km/s | 2. | 22.4 km/s |
3. | 5.6 km/s | 4. | 44.8 km/s |
Rohini satellite is at a height of 500 km and Insat-B is at a height of 3600 km from the surface of the earth. The relation between their orbital velocity (\(v_R,~v_i\)) is:
1. \(v_R>v_i\)
2. \(v_R<v_i\)
3. \(v_R=v_i\)
4. No relation
For moon, its mass is 1/81 of Earth's mass and its diameter is 1/3.7 of Earth's diameter. If acceleration due to gravity at Earth's surface is 9.8 m/, then at the moon, its value is:
1. | 2.86 m/s2 | 2. | 1.65 m/s2 |
3. | 8.65 m/s2 | 4. | 5.16 m/s2 |
Two spheres of masses \(m\) and \(M\) are situated in air and the gravitational force between them is \(F.\) If the space around the masses is filled with a liquid of specific density \(3,\) the gravitational force will become:
1. \(3F\)
2. \(F\)
3. \(F/3\)
4. \(F/9\)
A planet moves around the sun. At a point P, it is closest to the sun at a distance \(d_1\) and has speed \(v_1.\) At another point Q, when it is farthest from the sun at distance \(d_2,\) its speed will be:
1. | \(d_2v_1 \over d_1\) | 2. | \(d_1v_1 \over d_2\) |
3. | \(d_1^2v_1 \over d_2\) | 4. | \(d_2^2v_1 \over d_1\) |
The gravitational potential energy of an isolated system of three particles, each of mass \(\mathrm{m}\) placed at three corners of an equilateral triangle of side \(\mathrm{l}\) is:
1. | \(-Gm \over \mathrm{l}^2\) | 2. | \(-Gm^2 \over 2\mathrm{l}\) |
3. | \(-2Gm^2 \over \mathrm{l}\) | 4. | \(-3Gm^2 \over \mathrm{l}\) |
Two satellites S1 and S2 are revolving around a planet in coplanar and concentric circular orbits of radii R1 and R2 in the same direction respectively. Their respective periods of revolution are 1 hr and 8 hr. The radius of the orbit of satellite S1 is equal to 104 km. Find the relative speed when they are closest to each other.
1.
2.
3.
4.
A body of mass m is situated at a distance 4 above the Earth's surface, where is the radius of the Earth. What minimum energy should be given to the body so that it may escape?
1. | mgRe | 2. | 2mgRe |
3. | mgRe/5 | 4. | mgRe/16 |