Compute the mass of the earth, assuming it to be a sphere of radius 6370 km [using the concepts of gravitation]
Answers
Density of Earth 5510 kg / m^s
Volume = 4/3 π r^3
=4/3 π (6370×10^3)^3
Mass = volume× density
= 1.27 × 10^21 × 5510
= 7× 10^24 kg
The mass of earth is 6 × 10²⁴ kg.
We have to compute the mass of earth, assuming it to be a sphere of radius 6370 km [ Using the concepts of gravitation ]
Let an object of mass m is placed on the surface of earth, due to earth's gravitational field, a force of magnitude mg acting along the centre of earth.
i.e., weight of body = earth gravitational force acting on the object.
⇒ mg = GMm/R²
where,
- M is mass of earth
- R is the radius of earth. i.e., R = 6370 km = 6.37 × 10⁶ m [ given ]
- m is mass of object.
- g is acceleration due to gravity. ie., g = 9.8 m/s²
- G is gravitational constant i.e., G = 6.67 × 10⁻¹¹ Nm²/kg²
⇒ m × 9.8 = (6.67 × 10⁻¹¹ × M × m)/(6.37 × 10⁶)²
⇒ 9.8 × (6.37 × 10⁶)²/(6.67 × 10⁻¹¹) = M
⇒ M = 5.96182 × 10²⁴ kg ≈ 6 × 10²⁴ kg
Therefore the mass of earth is 6 × 10²⁴ kg.
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