The mass of the earth is 6x1024 kg and its radius is 6400 km. What is the mass of a man weighing 977N in the spring balance? (Universal gravitational constant is 6.67x10-11 Nm2/Kg2)
1 Answer
Given,
Mass of the earth (M) = 6 x 1024 Kg
Radius of the earth = 6400 Km = 6400000 m = 64 x 105 m = 6.4 x 106 m
Weight of the man (Gravitational force F) = 977 N
Mass of the man (m) = ?
Universal gravitational constant (G) = 6.67x10-11 Nm2/Kg2
According to the formula,
\(F=\frac{G\times m_1\times m_2}{d^2}\)
Or, \(977=\frac{6.67\times10^{-11}\times6\times10^{24}\times m}{{(6.4\times10^6)}^2}\)
∴ m = 99.99 kg
Hence the mass of man is 99.99 kg
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