Question

The escape speed from earth for a piece of 10 gram is 11.km/s.what be it for a piece of 100 gram

Answer 1

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

$\large\red{\boxed{\sf v_2=110\:km/s }}$

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

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

• Escape velocity $\sf({v_{1})=11 km/s}$

• Mass (m) = 10g

• Mass (M) = 100g

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

• Escape velocity for mass(M) 100g ($\sf{(v_2)=?}$

━━━━━━━━━━━━━━━━━━━━━━━━━

Escape velocity :

$\large{\boxed{\sf v_{escape}=\sqrt{\frac{2GM}{R}}}}$

Here we can see that escape velocity is directly proportional to mass

Therefore,

$\large\implies{\sf \frac{v_1}{v_2}=\sqrt{\frac{m}{M}}}$

$\large\implies{\sf \frac{11}{v_2}=\sqrt{\frac{1}{100}}}$

$\large\implies{\sf \frac{11}{v_2}=\frac{1}{10}}$

$\large\implies{\sf v_2=11×10}$

$\large\implies{\sf v_2=110\:km/s }$

$\large\red{\boxed{\sf v_2=110\:km/s }}$

Hence ,

Escape velocity for mass 100g is 110km/s