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

The gravitational intensity at the centre of a hemispherical shell of uniform mass density has the direction indicated by the arrow: 

1. a, d
2. b, d
3. c, e
4. d, e

A rocket is fired from the earth towards the sun. At what distance from the earth’s centre is the gravitational force on the rocket zero?

Given, the mass of the sun = $2\times {10}^{30}$ kg, the mass of the earth =  $6\times {10}^{24}$kg, and orbital radius = $1.5\times {10}^{11}$ m. Neglect the effect of other planets etc.
1. 2.59 × 10⁸ m
2. 3.10 × 10⁸ m
3. 4.07 × 10⁸ m
4. 2.23 × 10⁸ m

If the mean orbital radius of the earth around the sun is $1.5\times {10}^8 km$. Then the mass of the sun is approximately:
1. 3 × 10³⁴ kg
2. 2 × 10³⁰ kg
3. 1.5 × 10²⁸ kg
4. 1.0 × 10³⁵ kg

A Saturn year is 29.5 times the earth year. How far is Saturn from the sun if the earth is $1.5\times {10}^8 km$ away from the sun?
1. 2.01 × 10¹² m
2. 3.86 × 10¹² m
3. 1.43 × 10¹² m
4. 4.19 × 10¹² m

A body weights \(63\) N on the surface of the earth. What is the gravitational force on it due to the earth at a height equal to half the radius of the earth?
1. \(98~\text N\) 
2. \(35~\text N\) 
3. \(63~\text N\) 
4. \(28~\text N\) 

Assuming the earth to be a sphere of uniform mass density, how much would a body weigh halfway down to the centre of the earth if it weighed \(250\) N on the surface?

A rocket is fired vertically with a speed of \(5\) km/s from the earth’s surface. How far from the earth does the rocket go before returning to the earth?
1. \(8\times10^6\) m
2. \(1.6\times10^6\) m
3. \(6.4\times10^6\) m
4. \(12\times10^6\) m

The escape speed of a projectile on the earth’s surface is \(11.2\) km/s. A body is projected out with thrice this speed. What is the speed of the body far away from the earth?  (Ignore the presence of the sun and other planets.)
1. \(32.7\) km/s
2. \(11.2\) km/s
3. \(31.7\) km/s
4. \(21.2\) km/s

A satellite orbits the earth at a height of 400 km above the surface. How much energy must be expended to rocket the satellite out of the earth’s gravitational influence? (Mass of the satellite = 200 kg; mass of the earth = 6.0×${10}^{24}$ kg, radius of the earth = 6.4 × ${10}^6$ m, G = 6.67 × ${10}^{-11}$ $N m^2 k{g}^{-2}$)

1. 7.5 × 10⁹ J
2. 4.7 × 10⁹ J
3. 4.4 × 10⁹ J
4. 5.9 × 10⁹ J