Question

If the earth were made of wood, its mass would be 10% of its current mass. What would be the escape velocity, if the earth were made of wood?

Answer 1

we know, escape velocity , $v_e=\sqrt{2gR}$
where R is the radius of the earth, g is acceleration due to gravity.

from data, R = 6400km = 6.4 × 10^6 m
g = 9.8 m/s²

so, escape velocity , $v_e=\sqrt{2\times9.8\times6.4\times10^6}$ = 11.2 km/s

now, we also know, escape velocity is directly proportional to square root of mass of the earth,
so, $\frac{v_{ew}}{v_{ee}}=\sqrt{\frac{M_w}{M_e}}$

where, $v_{ew}$ indicates escape velocity of the earth made of wood.

given, $M_w$ = 10% of $M_e$ or 0.1$M_e$

so, $\frac{v_{ew}}{11.2}=\sqrt{\frac{0.1M_e}{M_e}}$

or, $v_{ew}=\frac{11.2}{\sqrt{10}}=3.536km/s$

hence, escape velocity of the earth made of wood is 3.536 km/s

Answer 2

Answer: thanks

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