Question

the mass and the density of Mars are 6.42×10^23kg and 3,940, respectively. what is the escape velocity? ​

Answer 1

SOLUTION

Let we through a body on the surface of earth at a speed of v

And this velocity is enough for a body to escape the gravitational field .It means it travels to infinity.

Potential energy of the particle at a height h can be written as....where h is measured from centre of earth.

U = -GMm/h

Initial energy of the body = 1/2mv² - GMm/R

Final energy at infinity = 1/2mu²

u is the speed at infinity.

Apply law of conservation of energy....

1/2mv² - GMm/R² = 1/2mu²

1/2mv² = 1/2mu² + GMm/R²

if we remove 1/2mu² term than the equals to sign changes because it's an positive quantity.

1/2mv² > GMm/R

v² > 2GM/R

v > √2GM/R

Volume = 4πR³/3 = 4.2R³

Density of Mars = 3940

Density = mass/volume

Mass = 6.42 × 10^23kg

3940 = 6.42 × 10^23 / 4.2R³

After calculation we get R = 3389.4km

Mass = 6.42 × 10^23kg

Put value in the EQUATION derived above.

v = √GM/R

G = 6.67 × 10^-11

We get v = 5km/sec (approx)

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Answer 2

Explanation:

we get velocity =5km/sec...approx..

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