If the radius of a planet is \(\mathrm{R}\) and its density is , the escape velocity from its surface will be:
1.
2.
3.
4.
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 |
A black hole is an object whose gravitational field is so strong that even light cannot escape from it. To what approximate radius would Earth (mass \(= 5.98\times 10^{24}~\text{kg}\)) have to be compressed to be a black hole?
1. \(10^{-9}~\text{m}\)
2. \(10^{-6}~\text{m}\)
3. \(10^{-2}~\text{m}\)
4. \(100~\text{m}\)
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 body is projected vertically upwards from the surface of a planet of radius R with a velocity equal to half the escape velocity for that planet. The maximum height attained by the body is:
1. R/3
2. R/2
3. R/4
4. R/5
A particle is located midway between two point masses each of mass \(\mathrm{M}\) kept at a separation \(2\mathrm{d}.\) The escape speed of the particle is: (neglect the effect of any other gravitational effect)
1.
2.
3.
4.