With what velocity should a particle be projected so that its hei… - Vidyadip

MCQ

With what velocity should a particle be projected so that its height becomes equal to radius of earth?

✓
$\left(\frac{G M}{R}\right)^{1 / 2}$
B
$\left(\frac{8 G M}{R}\right)^{1 / 2}$
C
$\left(\frac{2 G M}{R}\right)^{1 / 2}$
D
$\left(\frac{4 G M}{R}\right)^{1 / 2}$

✓

Answer

Correct option: A.

$\left(\frac{G M}{R}\right)^{1 / 2}$

a
$v^{2}=\frac{2 g h}{1+\frac{h}{R}}$

given $h=R$.

$v=\sqrt{g R}=\sqrt{\frac{G M}{R}} .$

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A.	Triatomic rigid gas	I.	$\frac{\mathrm{C}_{\mathrm{P}}}{\mathrm{C}_{\mathrm{V}}}=\frac{5}{3}$
B.	Diatomic non-rigid gas	II.	$\frac{\mathrm{C}_{\mathrm{P}}}{\mathrm{C}_{\mathrm{V}}}=\frac{7}{5}$
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