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 specific relation
For moon, its mass is \(\frac{1}{81}\) of Earth's mass and its diameter is \(\frac{1}{3.7}\) 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. \(F/9\)
1. | \(11.2\) km/s | 2. | \(22.4\) km/s |
3. | \(5.6\) km/s | 4. | \(44.8\) km/s |
1. | \(g' = 3g\) | 2. | \(g' = 9g\) |
3. | \(g' = \frac{g}{9}\) | 4. | \(g' = 27g\) |
1. | \(\dfrac R {n^2}\) | 2. | \(\dfrac {R~(n-1)} n\) |
3. | \(\dfrac {Rn} { (n-1)}\) | 4. | \(\dfrac R n\) |
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. | \(d_2^2v_1 \over d_1\) |
1. | \(-Gm \over {l}^2\) | 2. | \(-Gm^2 \over 2{l}\) |
3. | \(-2Gm^2 \over {l}\) | 4. | \(-3Gm^2 \over {l}\) |
Two satellites \(S_1\) and \(S_2\) are revolving around a planet in coplanar and concentric circular orbits of radii \(R_1\) and \(R_2\) in the same direction respectively. Their respective periods of revolution are \(1\) hr and \(8\) hr. The radius of the orbit of satellite \(S_1\) is equal to \(10^4\) km. Find the relative speed when they are closest to each other.
1. \(2\pi \times 10^4~\text{kmph}\)
2. \(\pi \times 10^4~\text{kmph}\)
3. \(\frac{\pi}{2} \times 10^4~\text{kmph}\)
4. \(\frac{\pi}{3} \times 10^4~\text{kmph}\)
1. | \(mgR_e\) | 2. | \(2mgR_e\) |
3. | \(\frac{mgR_e}{5}\) | 4. | \(\frac{mgR_e}{16}\) |