Question

If the force experienced by a body of unit mass is gravitational field strength, find thegravitational field strength on the surface of the earth.

Answer 1

Given that, The force experienced by a body of unit mass is gravitational field strength.

Now, We are to find Gravitational field strength on the earth.

By Newton's law of gravitation, We have the equation for force,

$F = \frac{Gm_{1}m_{2}}{ {r}^{2} }$

here, G is the universal gravitational constant. m1, m2 are the masses, r is the distance of separation.

In this case,

m1 = 1 kg ( Unit mass)

m2 = 6 * 10^24 kg ( Mass of earth)

r = 6400 * 10^3 ( Distance of separation = distance from center to surface.

G = 6.67 * 10^-11 m³ /kgs²

Now,

$F = \dfrac{6.67 \times {10}^{ - 11} \times 1 \times 6 \times {10}^{24} }{ {(6400 \times 10 ^{3} )}^{2} } \\ \\ \: \: \: \: \: = 0.0098 \times \frac{ {10}^{13} }{ {10}^{10} } = 9.8 N \:$

Therefore, The Gravitational field strength on the surface of earth is 9.8 N/kg.