Question

The gravitational force between two identical lead spheres kept at 1 m apart is
0.006673 N. Find their masses

Answer 1

Answer:

the mass is 6.67345×10^4

Answer 2

The mass of the lead sphere is 10⁴ or 10000 kg.

Given:
Distance between the lead spheres $=1m$

Force $=0.006673N$

To find:

Mass of the sphere.

Solution:

Newton's law of gravitation states that the gravitational force between two bodies (lets say) mass $M$ and $m$ separated by some finite distance lets say $R$ is directly proportional to the product of the two masses and is inversely proportional to the square of the distance by which the masses are separated.

$F$ ∝ $Mm$

$F$ ∝ $\frac{1}{R^{2} }$

$F$ ∝ $\frac{Mm}{R^{2} }$

$F=G\frac{Mm}{R^{2} }$

Where, $G$ is the Universal Gravitational constant whose value is

$G=6.673$ × $10^{-11}Nm^{2} /kg^{2}$

Now,

According to the question, we have been given that the masses of both the objects is same,

$M=m$     $;$ $and$

$R=1m$

$F=0.006673N$

Substituting the values in the given equation, we get

$F=G\frac{m.m}{R^{2} }$

$0.006673=\frac{6.673*10^{-11} *m^{2} }{(1)^{2} }$

$6.673*10^{-3}=6.673*10^{-11}*m^{2}$

$m^{2} =\frac{10^{-3} }{10^{-11} }$

$m^{2} =10^{8}$

$m=10^{4}kg$

Final answer:

Hence, the mass of the lead sphere is 10000 kg.