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03/11/2021 5:30 pm
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Suppose a planet exists whose mass and radius both are half those of the earth. Calculate the acceleration due to gravity on the surface of this planet.
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03/11/2021 5:38 pm
Acceleration due to gravity of earth,
g = \(G \times \frac{M}{R^2}\) = 9.8 m/s2
If mass of planet, m = \(\frac{M}{2}\)
And radius of planet, r = \(\frac{R}{2}\)
Acceleration due to gravity on the surface of planet will be:
g = \(G \times \frac{m}{r^2}\) .....(i)
m = \(\frac{M}{2}\) ......(ii)
r = \(\frac{R}{2}\) ......(iii)
Put (ii) and (iii) in (i) eq. we get
g = \(G \times \frac{\frac{M}{2}}{(\frac{R}{2})^2}\) = \(\frac{4}{2}\) x \((\frac{M}{R^2})\)
g = 2 x 9.8 m/s2
g = 19.6 m/s2