Acceleration due to gravity below and above the surface of earth MCQ Quiz - Objective Question with Answer for Acceleration due to gravity below and above the surface of earth - Download Free PDF

Calculation:

Acceleration due to gravity at h = R / 3

g′ = g / (1 + h / R_e)² = g / (1 + R_e / 3R_e)²

= g / (4 / 3)² = (9 / 16) × g

⇒ So w′ = 9 / 16

w = (9 / 16) × 48 = 36 N

Calculation:
The acceleration due to gravity at height h above the surface of the Earth is given by the formula:

g = g₀ × (R_E / (R_E + h))²

⇒ 2.5 = g₀ × (6400 / (6400 + 6400))²

g₀ = 2.5 × (2)² = 2.5 × 4 = 10 m/s²

Now, using this value of g₀, we can calculate the acceleration due to gravity at a height of 12800 km:

g = 10 × (6400 / (6400 + 12800))²

g = 10 × (6400 / 19200)² = 10 × (1 / 3)² = 10 × (1 / 9) = 1.11 m/s²

Answer: 1.11 m/s²

Explanation:

With depth

As depth goes on increasing goes on decreasing, it remains maximum at the surface of Earth. The above equation is in the form of straight line.

With height

(Hyperbola)

Acceleration due to gravity goes on decreasing as the above Earth surface increases.

Hence the correct answer is option A.

Effect of angular velocity on acceleration due to gravity is given by

so with increase in the decreases

but at poles ; so

CONCEPT:

• Acceleration due to gravity: The acceleration achieved by any object due to the gravitational force of attraction by any planet is called acceleration due to gravity by the earth.
  • As each planet has a different mass and radius so the acceleration due to gravity will be different for a different planet.

Acceleration due to gravity of earth having mass M on the surface of the earth is given by:

Acceleration due to gravity at height (h) above the earth’s surface is given by:

Where G is the Universal gravitational constant, R_e is the radius of the earth and h is the height

CALCULATION:

Given that:

g at the surface of the earth is 10 m/s2

At height h = R_e

g' = g/(1+1)² = g/4 = 10/4 = 2.5 m/s²

Hence option 2 is correct.

Concept:

Acceleration Due to Gravity:

• The force of attraction exerted by the earth on a body is called gravitational pull or gravity.
• We know that when a force acts on a body, it produces acceleration. Therefore, a body under the effect of gravitational pull must accelerate.
• The acceleration produced in the motion of a body under the effect of gravity is called acceleration due to gravity, it is denoted by g.

• The acceleration due to gravity on the surface is given as

⇒ 

Acceleration due to gravity at height

The acceleration due to gravity at height h is given, by simply adding R to g.

  ----(1)

It decreases with an increase in height. 

Acceleration due to gravity at depth

The acceleration due to gravity at depth d is given as 

        ----(2)

Explanation:

The value of acceleration due to gravity decreases as we go above the surface or below the surface.

So, the maximum value of g is at the surface of the earth.

The correct option is At the surface of earth.

CONCEPT:

Acceleration Due to Gravity:

• The force of attraction exerted by the earth on a body is called gravitational pull or gravity.
• We know that when a force acts on a body, it produces acceleration. Therefore, a body under the effect of gravitational pull must accelerate.
• The acceleration produced in the motion of a body under the effect of gravity is called acceleration due to gravity, it is denoted by g.
• If g is the acceleration due to gravity, then

Where G = universal gravitational constant, M = mass of the earth and R = radius of the earth

Weight:

• The weight of an object is defined as the force of gravity on the object and may be calculated as the mass times the acceleration of gravity, i.e.,

W = mg

Where m = mass of the object and g = acceleration due to gravity

CALCULATION:

Given - Weight of body at height (W') = mg', the weight of the body on the surface of earth (W) = mg and 

• Acceleration due to gravity at height h from the surface of the earth -

          ----------- (1)

Multiply both sides by m, then we get 

According to question, W' = W/16 

⇒ h = 3R

The correct option is 4.

CONCEPT:

• Acceleration due to gravity: The acceleration achieved by any object due to the gravitational force of attraction by any planet is called acceleration due to gravity by the earth.
  • As each planet has a different mass and radius so the acceleration due to gravity will be different for a different planet.

Acceleration due to the gravity of earth having mass M on the surface of the earth is given by:

Acceleration due to gravity at height (h) above the earth’s surface is given by:

Where G is the Universal gravitational constant, R is the radius of the earth and h is the height

CALCULATION:

Given that:

Acceleration due to gravity reduces by 75 %. 

So the acceleration due to gravity at height a height (h) = 25 % of g = 0.25 g = g/4

1 + h/R = 2

h/R = 1

Hence h = R

CONCEPT:

Kepler’s laws of planetary motion:

In the 16^th Century to explain the motion of planets, A German scientist Johannes Kepler first proposed his three laws of motion which were later termed as Kepler’s law of planetary motion.

• Kepler’s first law or the law of Orbits: Every planet moves around the sun in an elliptical orbit with the sun at one of the foci.
• Kepler’s second law or the law of Area: The line joining the sun to the planet sweeps out equal areas in equal interval of time. i.e. areal velocity is constant.

This diagram shows that areal velocity of satellite is constant for area A and B

• According to this law, the planet will move slowly when it is farthest from the sun and more rapidly when it is nearest to the sun. It is similar to the law of conservation of angular momentum.
• Kepler’s third law or the law of periods: The square of the period of revolution (T) of any planet around the sun is directly proportional to the cube of the semi-major axis of the orbit i.e. T² ∝ a³

EXPLANATION:

From the above given explanation, we can see that according to Kepler’s third law of planetary motion the time period of satellite’s or planet’s revolution depends on the distance of its semi major axis and it is given as  

The above diagram represents the motion of plant in an elliptical orbit around sun

Hence option 4 is correct among all.

Where,

Length of semi-major axis = a

The time period of the planet = T

Kepler’s constant = 

CONCEPT:

• The acceleration achieved by any object due to the gravitational force of attraction by any planet is called acceleration due to gravity by the earth.
• As each planet has a different mass and radius so the acceleration due to gravity will be different for different planets.
• Acceleration due to gravity of earth having mass M on the surface of the earth is given by:

• Acceleration due to gravity at height (h) above the earth’s surface is given by:

Where G = Universal gravitational constant, R = radius of the earth, and h = height

EXPLANATION:

Given that:

• Acceleration due to gravity at height h is (g') = g/4

⇒ (1 + h/R)² = 4

⇒ 1 + h/R = 2

⇒ h/R = 1

⇒  h = R

• Hence option 4 is correct.

CONCEPT:

Acceleration Due to Gravity:

• The force of attraction exerted by the earth on a body is called gravitational pull or gravity.
• We know that when a force acts on a body, it produces acceleration. Therefore, a body under the effect of gravitational pull must accelerate.
• The acceleration produced in the motion of a body under the effect of gravity is called acceleration due to gravity, it is denoted by g.
• The acceleration due to gravity on the surface of the earth is given by,

Where G = universal gravitational constant, M = mass of the earth and R = radius of the earth

CALCULATION:

Given - Acceleration due to gravity at height h from the surface of the earth (g_h) = 1/9th (g_e)

• The acceleration due to gravity on the surface of the earth is given by,

         ----------- (1)

• Acceleration due to gravity at height h from the surface of the earth -

          ----------- (2)

On dividing equations 1 and 2, we get

On square rooting both side, we get

⇒ 3R = R + h

⇒ 2R = h

CONCEPT:​

• Gravitational acceleration: An acceleration that an object receives due to the force of gravity acting on it.
• Gravitational Acceleration: It is calculated by using the formula

where g is the gravitational acceleration, G is the gravitational constant, M is the mass of the earth and R is the radius of the earth.

• When an object is at depth 'd', gravitational acceleration: It is calculated by

where g_d is the gravitational acceleration at depth d, g is the gravitational acceleration at the surface, and R is the radius of the earth.

EXPLANATION:

Gravitational acceleration at the depth d is given by

As we go below the earth's surface, the depth 'd' will increase.

As d increases,  will decrease.

As  decreases,  will also decrease.

So g_d will decrease with depth.

• So as we go below the earth's surface, the gravitational acceleration decreases.
• Hence the correct answer is option 1.

Concept:

• Acceleration due to gravity: The acceleration achieved by any object due to the gravitational force of attraction by the earth is called acceleration due to gravity by the earth.
  • As each planet has a different mass and radius so the acceleration due to gravity will be different for a different planet.

Acceleration due to gravity of the earth having mass (M) and radius (R) on earth surface is given by:

Here G is the universal gravitational constant.

Acceleration due to gravity at any depth (h) of the earth’s surface whose distance from the centre of the earth is r is given by:

Acceleration due to gravity at height (h’) whose distance from the centre of the earth is r is given by:

Where G is Universal gravitational constant, r = (R - h) and r’ = (R + h).

Calculation:

New Gravity above the surface of earth g' :

When h = R_e

Alternate Method Acceleration due to gravity = 

R = distance from the centre of the earth.

At a height = R above the earth's surface

The correct answer is option 1) i.e. increases with increase in latitude

CONCEPT:

• Law of Universal Gravitation: It states that all objects attract each other with a force that is proportional to the masses of two objects and inversely proportional to the square of the distance that separates their centres.

It is given mathematically as follows:

Where m1 and m2 are the mass of two objects, G is the gravitational constant and R is the distance between their centres.

• From the Law of Universal Gravitation, the gravitational force acting on an object of mass m placed on the surface of Earth is:

Where R is the radius of the earth. 

From Newton's second law, F = ma = mg

⇒ Acceleration due to gravity, 

EXPLANATION:

• The latitude of a point is the angle between the equatorial plane and line joining that point to the centre of the earth.
• The latitude of the equator is 0^∘ and the latitude of poles is 90^∘. 
• We know that the earth is not a perfect sphere, but it is bulged outwards towards the equator.

From the relation , the value of R is greater at the equator than at the poles.

• Hence, the acceleration due to gravity increases towards the poles.
• So, as we move from the equator to the poles, the latitude increases and the acceleration due to gravity increases.
• Thus, acceleration due to gravity increases with an increase in latitude.