Question

plz solve it
Its urgent ​

Answer 1

$\huge\underline\blue{\sf Answer:}$

$\large\red{\boxed{\sf v_w=3.54m/s}}$

$\huge\underline\blue{\sf Solution:}$

$\large\underline\pink{\sf Given: }$

• Mass of wooden earth $\sf{M_w}$ is 10% of mass of original earth $\sf{M_e}$

We know ,

• Radius of Earth (R) = 6400km or $\sf{6.4×10^6}$m

$\large\underline\pink{\sf To\:Find: }$

• Escape velocity of wooden earth ($\sf{v_w}$)=?

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We know that ,

$\large\underline{\underline{\sf Escape\: Velocity\:of\:Earth(v_e):}}$

$\large{\boxed{\sf v_e=\sqrt{\frac{2GM_e}{R_e}}}}$

$\large{\sf g=\sqrt{\frac{GM_e}{R_e^2}}}$

g of Earth is = 10 $\sf{m/s^2}$

$\large{\sf v_e=\sqrt{2gR}}$

$\large\implies{\sf v_e=\sqrt{2×10×6.4×10^6} }$

$\large\implies{\sf v_e=11.2\:m/s}$

Escape velocity of Earth is 11.2m/s

From here we can see that escape velocity is directly proportional to Mass of Earth .

So ,

$\large\implies{\sf \frac{v_w}{v_e}=\sqrt{\frac{M_e}{M_w}}}$

$\large\implies{\sf \frac{v_w}{11.2}=\sqrt{\frac{M_e×10}{M_e×100}}}$

$\large\implies{\sf \frac{v_w}{11.2}=\frac{1}{\sqrt{10}}}$

$\large\implies{\sf v_w=\frac{11.2}{\sqrt{10}}}$

$\large\implies{\sf v_w=3.54m/s }$

$\large\red{\boxed{\sf v_w=3.54m/s}}$

Hence ,

Escape velocity of wooden earth will be 3.54m/s