Question

Determine the SI unit of the universal constant of gravitation from the formula for the gravitational force between two particles and state the CGS unit of the constant of gravitation define G universal gravitational constant.​

Answer 1

Gravitational force=GMm/r^2

G - gravitational constant

M - mass of 1st object

m - mass of 2nd object

r - distance between the objects

G=Fr^2/Mm

SI unit of G=kg-1 m2 s-1

Dimensions=M-1 L2 T-1

CGS unit=g-1 cm2 s-1

G(universal gravitational constant) is the constant for the gravitational force all over the world which never changes....

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Answer 2

Question ➛

i. Determine the SI unit of the universal constant of gravitation from the formula for the gravitational force between two particles and state the CGS unit of the constant of gravitation.

ii. define G (universal gravitational constant) .

Answer ➛

i) According to Newton's law of gravitation, the gravitational force between two particles is ➛

$\\ \: \: \: \: \: \: \: \: \: \: \: \: \quad\bf{ \pink{F = G \frac{ m_{1}m_{2}}{r ^{2} } }}$

Where, m1 and m2 are the masses of the two particles, r is the distance between them and G is the universal constant of gravitation.

$\\ \: \: \: \: \: \: \: \: \: \: \: \quad\bf{ \pink{ \: ∵ G = \frac{F \: r ^{2} }{ m_{1}m_{2} } }}$

The SI unit of force is the Newton ( N ) , That of distance is the metre ( m ) and that of mass is the kilogram ( Kg ).

$\\ \: \: \quad\bf{ \pink{∵ \:The \: SI \: unit \: of \: G \: is \: \frac{N.m ^{2} }{Kg ^{2} } }} \\ \\ \: \: \quad\bf{ \pink{The \:CGS \: unit \: of \: G \: is \: \frac{dyne.cm ^{2} }{ {g}^{2} } }}$

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ii)

$\\ \: \: \: \: \: \: \: \: \: \: \: \: \quad\bf{ \pink{F = G \frac{ m_{1}m_{2}}{r ^{2} } }} \\ \\ \: \\ \: \: \: \: \: \: \: \: \: \: \: \quad\bf{ \pink{ \: ∵ G = \frac{F \: r ^{2} }{ m_{1}m_{2} } }}$

So, If we take m1 = m2 = Unit mass and r = unit distance, Then, G = F, i.e., G (Universal gravitational constant) Represents the magnitude of thr gravitational force of attraction between two unit masses, separated by a unit distance.

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