In planetary motion, the areal velocity of the position vector of a planet depends on the angular velocity () and the distance of the planet from the sun (r). The correct relation for areal velocity is:
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2.
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4.
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. | \(AM^2\) |
Magnitude of potential energy (U) and time period (T) of a satellite are related to each other as:
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A point P lies on the axis of a ring of mass M and radius 'a' at a distance 'a' from its centre C. A small particle starts from P and reaches C under gravitational attraction. Its speed at C will be :
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2.
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4. zero
A planet is moving in an elliptical orbit. If T, V, E, and L stand, respectively, for its kinetic energy, gravitational potential energy, total energy and angular momentum about the center of the orbit, then:
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 |
A projectile is fired upwards from the surface of the earth with a velocity where 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. \(\frac{2R}{1+k^2}\)
A satellite is moving very close to a planet of density . The time period of the satellite is:
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2.
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4.
A projectile is fired from the surface of the earth with a velocity of 5 m/s and angle with the horizontal. Another projectile fired from another planet with a velocity of 3 m/s at the same angle follows a trajectory of the projectile fired from the earth. The value of the acceleration due to gravity on the planet (in ms-2) is: (given, g=9.8 ms-2)
1. | 3.5 | 2. | 5.9 |
3. | 16.3 | 4. | 110.8 |
The escape velocity for a rocket from the earth is \(11.2\) km/s. Its value on a planet where the acceleration due to gravity is double that on the earth and the diameter of the planet is twice that of the earth (in km/s) will be:
1. | \(11.2\) | 2. | \(5.6\) |
3. | \(22.4\) | 4. | \(53.6\) |
For the moon to cease as the earth's satellite, its orbital velocity has to be increased by a factor of -
1. | 2 | 2. | \(\sqrt{2}\) |
3. | \(1/\sqrt{2}\) | 4. | 4 |