A satellite is moving very close to a planet of density \(\rho.\) The time period of the satellite is:
1. \(\sqrt{\frac{3 \pi}{ρG}}\)
2. \(\left(\frac{3 \pi}{ρG}\right)^{3 / 2}\)
3. \(\sqrt{\frac{3 \pi}{2 ρG}}\)
4. \(\left(\frac{3 \pi}{2 ρG}\right)^{3 / 2}\)
A projectile is fired upwards from the surface of the earth with a velocity \(kv_e\) where \(v_e\) is the escape velocity and \(k<1\). If \(r\) is the maximum distance from the center of the earth to which it rises and \(R\) is the radius of the earth, then \(r\) equals:
1. \(\frac{R}{k^2}\)
2. \(\frac{R}{1-k^2}\)
3. \(\frac{2R}{1-k^2}\)
4. \(\frac{2R}{1+k^2}\)
The gravitational potential difference between the surface of a planet and 10 m above is 5 J/kg. If the gravitational field is supposed to be uniform, the work done in moving a 2 kg mass from the surface of the planet to a height of 8 m is
1. 2J
2. 4J
3. 6J
4. 8J
1. | \(T\) is conserved |
2. | \(V\) is always positive |
3. | \(E\) is always negative |
4. | the magnitude of \(L\) is conserved but its direction changes continuously |
In planetary motion, the areal velocity of the position vector of a planet depends on the angular velocity \((\omega)\) and the distance of the planet from the sun \((r)\). The correct relation for areal velocity is:
1. \(\frac{dA}{dt}\propto \omega r\)
2. \(\frac{dA}{dt}\propto \omega^2 r\)
3. \(\frac{dA}{dt}\propto \omega r^2\)
4. \(\frac{dA}{dt}\propto \sqrt{\omega r}\)
If \(A\) is the areal velocity of a planet of mass \(M,\) then its angular momentum is:
1. | \(\frac{M}{A}\) | 2. | \(2MA\) |
3. | \(A^2M\) | 4. | \(AM^2\) |
Two bodies of masses m and 4m are placed at a distance r. The gravitational potential at a point on the line joining them where the gravitational field is zero is
1.
2.
3.
4. 0
Magnitude of potential energy (\(U\)) and time period \((T)\) of a satellite are related to each other as:
1. \(T^2\propto \frac{1}{U^{3}}\)
2. \(T\propto \frac{1}{U^{3}}\)
3. \(T^2\propto U^3\)
4. \(T^2\propto \frac{1}{U^{2}}\)
A projectile fired vertically upwards with a speed v escapes from the earth. If it is to be fired at 45 to the horizontal, what should be its speed so that it escapes from the earth?
1. v
2.
3.
4. 2v
Kepler's second law regarding constancy of the areal velocity of a planet is a consequence of the law of conservation of:
1. Energy
2. Linear momentum
3. Angular momentum
4. Mass