Advertisements
Advertisements
Question
How is acceleration due to gravity-related to
- mass of a planet
- distance of body from the center of the earth?
Advertisements
Solution
Acceleration due to gravity: The acceleration of a freely falling body, under the action of gravity of earth, is called acceleration due to gravity.
Consider a body of mass ‘m’ on the surface of the earth such that it falls towards it with an acceleration ‘g’.
Let, M = mass of the earth
d = distance between center of earth and center of the body
F = Force acting on the body
F = mg .............(i)
F = `"G""Mm"/"d"^2` ...............(ii)
Comparing (i) and (ii)
mg = `"G""Mm"/"d"^2`
g = `"Gm"/"d"^2`
From this equation, it is clear that
1. g α M
Acceleration due to gravity on the earth is directly proportional to the mass of that earth.
2. g α `1/"d"^2`
Acceleration due to gravity is inversely proportional to the square of the distance of the body from centre of the earth.
APPEARS IN
RELATED QUESTIONS
In the Figure a block of weight 15 N is hanging from a rigid support by a string. What force is exerted by (a) a block on the string and (b) a string on the block? Name and show them in the diagram.
What do you understand by the term force due to gravity ?
The weight of a body is 2.0 N. What is the mass of the body? (g = 10 m s-2)
State two important characteristics of weight
State the unit of weight in SI system.
A man weigh 800 N at the equator. How does the weight of man change at the following place?
At poles
How is weight affected in the following case, when initially the body is weighed in Delhi with a spring balance?
Body is taken to Moscow.
How is weight affected in the following case, when initially the body is weighed in Delhi with a spring balance?
Body is taken to Ceylon.
Where will a person weigh more: at Simla or at Delhi?
A cricket ball of mass 500 g moving at a speed of 30 ms 1 is brought to rest by a player in 0.03 s. Find the average force applied by the player.
