Gravitational field

(A) Concept of gravitational field

Earth gravitational field

Source: www.commons.wikimedia.org 

Newton’s law of gravitation

This law states that every particle of matter in the universe attracts every other particle with a force that is directly proportional to the product of the masses of the particles and inversely proportional to the square of the distance between them. F=Gm₁m₂ / r²

Gravitational attraction between masses

Source: www.en.wikipedia.org

Variation gravity of earth

Source: www.en.wikipedia.com

Weightlessness is a feeling of having no weight. At that time the gravitational pull of the earth has no effect on the body. A body experiences weightlessness at a certain height above the surface of the earth. At a particular altitude ‘h’ which is equal to half of the radius R of the earth, the acceleration due to gravity on the body is zero. Weightlessness can be discovered or experienced when a body is in a lift or an aeroplane descending. If a lift is descending with an acceleration ‘a’ the equation of motion is given as

             W-R = ma

Where  W = the weight of the man 

            R = the reaction on his feet

            m = the mass of the man

R= W-ma = mg-ma =m(g-a) thus, R = 0, when g=a

(B)Gravitational potential

The potential, V, at a point due to the Gravitational field of the earth is defined as numerically equal to the work done in taking a unit mass from infinity to that point.     V = -GM/r

Where V is the gravitational potential, M =mass of the earth, r = distance from the Centre of the earth.

Note: Velocity of escape, v = √(2gR)

Satellites is been expressed as 

mv²/ r    = GMm/r² = mg and v= √rg

Parking orbits is expressed as 

     mv² /R = GMm/R²

But GM = gr² (from 1) where r= radius of the earth. And v= √gr²/ R

If the period of the satellite in orbit B is T₁ , then. T₁² = 4π²R³ / gr²

Past questions

1. A body is projected from the Earth’s surface with the intention of letting it escape from the Earth’s gravitational field. What is the minimum escape velocity of the body? (Jamb 1995)

A. 14km/s

B. 13km/s

C. 12km/s

D. 11km/s [Earth’s radius= 6.4 × 10³km, g= 10ms^-2]

Answer: D

Solution: Velocity = √2gR = 2×6400×100×10= 11km/s

2. A man standing on a lift that is descending does not feel any weight  because? (Jamb 2011)

A. There is no reaction from the floor of the lift

B. There is no gravitational pull on the man in the lift

C. The inside of the lift is airtight

D. The lift is in vacuum

Answer: A

Solution: a body feels zero weight because the weight of acceleration of the lift is equal to acceleration due to gravity.

3. A rocket is fired from the Earth’s surface to a distant planet. By Newton’s law of universal gravitation, the force F will ?

(Jamb 2012)

A. Increase as r reduces

B. Increase as G varies

C. Remains constant

D. Increases as r increases

Answer: A

4. Calculate the apparent weight loss of a man weighing 70kg in an elevator moving downwards with an acceleration of 1.5ms^-2. (Jamb 2013)

A. 686N

B. 595N

C. 581N

D. 105N. [g= 10ms^-2]

Answer: D

Solution: wt loss = mg-m(g-a)

                 = 70×10-70(10-1.5) = 105N

5. The region around a magnet in which magnetic force can be experienced is known as ? (Wassce 2015)

A. Declination

B. Flux density

C. Field

D. Flux

Answer: C

6. In the absence of Gravitational force, the weight of a body is? ( Wassce 2011)

A. It’s mass 

B. Zero

C. Its density

D. Its volume

Answer: B

Solution: when there is no effect of Gravitational force on a body the weight of the body, can not be determined.

7. The correct relationship between G and g in a gravitational field is given by the equation (where the symbols have their usual meanings). (Wassce 2011)

A. g=  GM/R

B. g= GM/R²

C. g= GM²/R

D. g= GM²/R²

Answer: B

8. A satellite in circular motion around the earth does not have? (Wassce 2009)

A. A gravitational forces acting on it

B. A uniform Velocity

C. An acceleration

D. A centripetal force acting on it 

Answer: B