Read the given passage and answer the questions based on the passage and related concepts: The universal law of gravitation was proposed by Sir Issac Newton which is widely accepted to find the magnitude of attractive gravitational force between any two bodies in the universe. Greater the distance between bodies, weaker is the gravitational force between them and vice versa. Two bodies attract each other irrespective of their individual masses as gravitational force is directly proportional to the product of their masses and inversely proportional to the square of the distance of separation between them. Q (i) How does the gravitational force change if the mass of object is halved? Q(ii) What will happen to the gravitational force if the distance between the objects is doubled.
Answers
Answer:
The Law of Universal Gravitation
Objects with mass feel an attractive force that is proportional to their masses and inversely proportional to the square of the distance.
LEARNING OBJECTIVES
Express the Law of Universal Gravitation in mathematical form
KEY TAKEAWAYS
Key Points
Sir Isaac Newton’s inspiration for the Law of Universal Gravitation was from the dropping of an apple from a tree.
Newton’s insight on the inverse-square property of gravitational force was from intuition about the motion of the earth and the moon.
The mathematical formula for gravitational force is
F
=
G
Mm
r
2
where
G
is the gravitational constant.
Key Terms
induction: Use inductive reasoning to generalize and interpret results from applying Newton’s Law of Gravitation.
inverse: Opposite in effect or nature or order.
While an apple might not have struck Sir Isaac Newton’s head as myth suggests, the falling of one did inspire Newton to one of the great discoveries in mechanics: The Law of Universal Gravitation. Pondering why the apple never drops sideways or upwards or any other direction except perpendicular to the ground, Newton realized that the Earth itself must be responsible for the apple’s downward motion.
Theorizing that this force must be proportional to the masses of the two objects involved, and using previous intuition about the inverse-square relationship of the force between the earth and the moon, Newton was able to formulate a general physical law by induction.
The Law of Universal Gravitation states that every point mass attracts every other point mass in the universe by a force pointing in a straight line between the centers-of-mass of both points, and this force is proportional to the masses of the objects and inversely proportional to their separation This attractive force always points inward, from one point to the other. The Law applies to all objects with masses, big or small. Two big objects can be considered as point-like masses, if the distance between them is very large compared to their sizes or if they are spherically symmetric. For these cases the mass of each object can be represented as a point mass located at its center-of-mass.
While Newton was able to articulate his Law of Universal Gravitation and verify it experimentally, he could only calculate the relative gravitational force in comparison to another force. It wasn’t until Henry Cavendish’s verification of the gravitational constant that the Law of Universal Gravitation received its final algebraic form:
F
=
G
Mm
r
2
where
F
represents the force in Newtons,
M
and
m
represent the two masses in kilograms, and
r
represents the separation in meters.
G
represents the gravitational constant, which has a value of
6.674
⋅
10
−
11
N
(m/kg)
2
. Because of the magnitude of
G
, gravitational force is very small unless large masses are involved.