A. The value of G on the moon is equal to that on the earth.
B. $26.68 \times 10^{-11}$ N is the force of gravitation between two point masses of 2 kg and 2 kg kept 1 m apart.
C. Newton's law of gravitation is valid in the laboratory only.
D. Force is inversely proportional to the square of the distance between two bodies.
Gravitation Statements Analysis
This section analyzes the given statements related to Newton's law of gravitation to identify the incorrect ones.
G Constant Check
The universal gravitational constant, denoted by G, is a fundamental constant. Its value remains the same regardless of location, whether on the Moon or the Earth. Thus, the statement "The value of G on the moon is equal to that on the earth" is correct.
Force Calculation Verification
Newton's law of gravitation defines the force $F$ between two masses $m_1$ and $m_2$ separated by distance $r$ as:
$F = G \frac{m_1 m_2}{r^2}$
Using the provided values: $m_1 = 2$ kg, $m_2 = 2$ kg, $r = 1$ m, and the approximate value of $G = 6.67 \times 10^{-11}$ N m$^2$/kg$^2$.
Calculation:
$F = (6.67 \times 10^{-11} \text{ N m}^2/\text{kg}^2) \times \frac{(2 \text{ kg}) \times (2 \text{ kg})}{(1 \text{ m})^2}$
$F = (6.67 \times 10^{-11}) \times 4 \text{ N}$
$F = 26.68 \times 10^{-11} \text{ N}$
The calculated force matches the value stated, making this statement correct.
Law Validity Scope
Newton's law of gravitation is a universal principle, applicable everywhere in the universe, not confined solely to laboratory settings. Therefore, the statement "Newton's law of gravitation is valid in the laboratory only" is incorrect.
Distance-Force Relation
The gravitational force $F$ is described by $F = G \frac{m_1 m_2}{r^2}$. This equation shows that $F$ is proportional to $1/r^2$, meaning the force is inversely proportional to the square of the distance between the bodies. This statement is correct.
Incorrect Statement Identification
After evaluating each statement, only statement C is found to be incorrect.
Similar Questions
The gravitational force between two objects of masses m1 and m2 is directly proportional to
The force exerted by the earth on the moon is:
(Consider G=\(6 \times 10^{-11}Nm^2kg^{-2}\) ; mass of the earth M=\(6 \times 10^{24}\)kg; mass of the moon= \(8 \times 10^{22}\) kg, and distance between earth and moon is \(4 \times 10^{8}\) m).Which of the following statements is/are correct?
Statements:
I) The mass of an object is the same as its weight.
II) The mass of an object is not the same as its weight.
III) Mass is scalar quantity, whereas weight is vector quantity.
Which of the following statements is/are correct?
Statements:
I) The Gravitational force between two objects is independent of the distance of separation between two objects.
II) The Gravitational force between two objects is inversely proportional to the square of the distance of the separation between two objects.
III) The Gravitational force between two objects is directly proportional to the product of their masses.
When an object falls under gravity, the object experiences:
If the acceleration due to gravity of the earth is 6 times the acceleration due to gravity on the moon, which of the following statements is correct?
Energy possessed by a body by virtue of its position or configuration is:
- What will be the force of attraction between two bodies weighing 20 kg and 50 kg, respectively, with a distance of 2 metre between them?
Important Questions from Gravitation
The known forces of nature can be divided into four classes, viz., gravity, electromagnetism, weak nuclear force and strong nuclear force. With reference to them, which one of the following statements is not correct?
- A spacecraft of mass m = 1000 kg has a fully reflecting sail that is oriented perpendicular to the direction of the sun. The sun radiates 10 26 W and has a mass M = 10 30 kg. Ignoring the effect of the planets, for the gravitational pull of the sun to balance the radiation pressure on the sail, the area of the sail will be
The force of attraction between two bodies separated by a distance of d is F. The distance for which the force of attraction between them is 64 F is ________.
If two satellites of masses m1 and m2 are revolving around a earth in a circular orbits of radius r1 and r2, then the ratio of their orbital velocities \(\dfrac{v_1}{v_2}\) is
A women whose mass is 60 kg on the earth surface is in an spacecraft at an altitude of two times the earth radius. Her mass there is
