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The gravitational constant G was first measured accurately by Henry Cavendish in 1798. He used an exquisitely sensitive balance to measure the force between two lead spheres whose centers were 0.19 m apart. One of the spheres had a mass of 188 kg, while the mass of the other sphere was 0.63 kg. What was the ratio of the gravitational force between these spheres to the weight of the lighter sphere?

Respuesta :

Answer:

[tex]\dfrac{F_g}{W}=3.54\times 10^{-8}[/tex]

Explanation:

given,

distance between two led sphere = 0.19 m

mass of sphere

m₁ = 188 Kg

m₂ = 0.63 Kg

ratio of gravitational force between to the weight of light sphere

[tex]F_g = \dfrac{GMm}{r^2}[/tex]

W = m g

now,

[tex]\dfrac{F_g}{W}=\dfrac{\dfrac{GMm}{r^2}}{mg}[/tex]

[tex]\dfrac{F_g}{W}=\dfrac{GM}{r^2g}[/tex]

[tex]\dfrac{F_g}{W}=\dfrac{6.67 \times 10^{-11}\times 188}{0.19^2\times 9.8}[/tex]

[tex]\dfrac{F_g}{W}=3.54\times 10^{-8}[/tex]

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