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

Question

With what velocity should a particle be projected so that its height becomes equal to radius of earth? (A) ((G M/R))1 / 2 (B) ((8 G M/R))1 / 2 (C) ((2 G M/R))1 / 2 (D) ((4 G M/R))1 / 2

Tardigrade Admin · Accepted Answer

Use v2=(2 g h/1+(h)R) given h = R ∴ v=√g R=√(G M/R)

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

$(\frac{GM}{R})^{1/2}$

$(\frac{8 GM}{R})^{1/2}$

$(\frac{2 GM}{R})^{1/2}$

$(\frac{4 GM}{R})^{1/2}$

Use $v^{2} = \frac{2 g h}{1 + \frac{h}{R}}$ given $h = R$
$∴ v = g R = \frac{GM}{R}$

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

(RGM​)1/2

(R8GM​)1/2

(R2GM​)1/2

(R4GM​)1/2

Use v2=1+Rh​2gh​ given h=R ∴v=gR​=RGM​​

$(\frac{GM}{R})^{1/2}$

$(\frac{8 GM}{R})^{1/2}$

$(\frac{2 GM}{R})^{1/2}$

$(\frac{4 GM}{R})^{1/2}$

Use $v^{2} = \frac{2 g h}{1 + \frac{h}{R}}$ given $h = R$
$∴ v = g R = \frac{GM}{R}$