Question

The force of gravitation between two bodies of mass 1 kg each separated by a distance of $1 \mathrm{m}$ in vacuum is
A $\quad 6.67 \times 10^{-11} N$
В $\quad 6.67 \times 10^{-10} \boldsymbol{N}$
C $\quad 6.67 \times 10^{-9} N$
D $\quad 6.67 \times 10^{11} N$

Answer 1

Hint: We know that Newton's law of universal gravitation is usually stated as that every particle attracts every other particle in the universe with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between their centres. Since the gravitational force is directly proportional to the mass of both interacting objects, more massive objects will attract each other with a greater gravitational force. So as the mass of either object increases, the force of gravitational attraction between them also increases. Based on this we have to solve this question.

Complete step by step answer
Let us start the answer by mentioning the facts that are mentioned in the question:
 $\mathrm{m}_{1}=\mathrm{m}_{2}=1 \mathrm{kg}, \mathrm{r}=1 \mathrm{m}$
We have to find the force of gravitation now: The formula is written as:
Force of gravitation $\mathrm{F}=\dfrac{\mathrm{Gm}_{1} \mathrm{m}_{2}}{\mathrm{r}^{2}}$
In the above expression:
F is the gravitational force
G is the gravitational proportional constant
and ${{m}_{1}},{{m}_{2}}$are the masses of the two bodies that are mentioned.
So now we have to put the values in the above expression:
$\mathrm{F}=\dfrac{6.67 \times 10^{-11} \times 1 \times 1}{1^{2}}=6.67 \times 10^{-11} \mathrm{N}$
Hence, we can say that the gravitational force of attraction is $6.67\times {{10}^{-11}}N$

Hence the correct option is option A.

Note We know that there are three laws of gravitational force of attraction. In the first law, an object will not change its motion unless a force acts on it. In the second law, the force on an object is equal to its mass times its acceleration. In the third law, when two objects interact, they apply forces to each other of equal magnitude and opposite direction.
It should be known that the strength of the gravitational force between two objects depends on two factors, mass and distance. the force of gravity the masses exert on each other. If one of the masses is doubled, the force of gravity between the objects is doubled. increases, the force of gravity decreases.