Question

On the surface of the earth, the force of gravitational attraction between two masses kept at distance $d$ apart is $6N$. If these two masses are taken to the surface of moon and kept at the small distance $d$, the force between them will be
A. $1N$
B. $36N$
C. $\dfrac{1}{6}N$
D. $6N$

Answer 1

Hint:Let us firstly revise our concepts for gravitational attraction. Gravitational force is the force which is inserted to attract two objects. It is being created due to gravity. Gravitational force depends on two factors which are masses of two objects and the distance between the two objects.

Complete step by step answer:
Mathematically, gravitational force is defined as the force which is proportional to the product of masses of the objects and inversely proportional to distance between them. To remove the proportionality, we had added a constant which is known as a gravitational constant represented by $G$ whose value is $6.674 \times {10^{ - 11}}Nmk{g^{ - 1}}$.
Formula for gravitational force $F = G\dfrac{{{m_1}{m_2}}}{{{r^2}}}$
Where ${m_1}$ and ${m_2}$ are the masses of the two objects and $r$ is the distance between the two objects.

Now going back to the question where we are given that on the earth gravitational force between two masses is $6N$and we want to know the force on the moon.Since from the above definition of the gravitational force which only depends on the masses and the distance. On the moon we haven’t changed either masses of the two objects or the distance between the two. Hence, the force on moon should remain unchanged i.e.,$6N$

So, the correct option should be D.

Note:Every object that has mass can exert a gravitational force to another object with mass. The force between them will depend on the masses of the two objects. The acceleration due to gravity on the surface of moon is about $1.625m{s^{ - 1}}$ while on the earth is $9.8m{s^{ - 1}}$ hence acceleration on moon is about $16.6$ times that on the earth.