What is the depth at which the value of acceleration due to gravity becomes 1/n times the value of that at the surface of the earth? (radius of earth = R)

(1) R/${\mathrm{n}}^2$

(2) R(n – 1)/n

(3) Rn/(n – 1)

(4) R/n

Choose the correct alternative.

Acceleration due to gravity is:

Suppose there existed a planet that went around the sun twice as fast as the earth. Then its orbital size as compared to that of the earth would be:

1. 0.63 times greater than that of earth.
2. 0.73 times smaller than that of earth.
3. 0.63 times smaller than that of earth.
4. 0.73 times greater than that of earth.

One of the satellites of Jupiter has an orbital period of \(1.769\) days and the radius of the orbit is \(4.22 \times 10^{8}\) m. The ratio of the mass of Jupiter and the mass of the sun nearly is:
1. \(1000:1\)
2. \(1:1000\)
3. \(1:1\)
4. \(2000:3\)

Choose the correct alternative.

Let us assume that our galaxy consists of 2.5 × ${10}^{11}$ stars each of one solar mass. How long will a star at a distance of 50,000 ly from the galactic centre take to complete one revolution? (The diameter of the milky way is ${10}^5$ ly.)
1. 3.55 × 10⁸ years
2. 4.55 × 10⁸ years
3. 3.55 × 10⁷ years
4. 4.55 × 10⁷ years

The escape speed of a body from the earth depends on:

1. the mass of the body.
2. the location from where it is projected.
3. the direction of projection.
4. the height of the location from where the body is launched.

A comet orbits the sun in a highly elliptical orbit. The comet has a constant:
1. linear speed
2. angular speed
3. angular momentum
4. kinetic energy

Which of the following symptoms is not likely to afflict an astronaut in space?

1. swollen feet
2. swollen face
3. headache
4. orientational problem