A rocket of mass M is launched vertically from the surface of the earth with an initial speed V. Assuming the radius of the earth to be R and negligible air resistance, the maximum height attained by the rocket above the surface of the earth is

Question

A rocket of mass M is launched vertically from the surface of the earth with an initial speed V. Assuming the radius of the earth to be R and negligible air resistance, the maximum height attained by the rocket above the surface of the earth is (A) R /((g R/2 V2)-1) (B) R((g R/2 V2)-1) (C) R /((2 g R/V2)-1) (D) R((2 g R/V2)-1)

Tardigrade Admin · Accepted Answer

Δ K . E .=Δ U ⇒ (1/2) M V2=G Me M((1/R)-(1/R+h)) ...(i) Also g=(G Me/R2) ...(ii) On solving (i) and (ii), h=(R/((2 g R)V2-1))

Q. A rocket of mass $M$ is launched vertically from the surface of the earth with an initial speed $V$ . Assuming the radius of the earth to be $R$ and negligible air resistance, the maximum height attained by the rocket above the surface of the earth is

$R / (\frac{g R}{2 V ^{2}} - 1)$

$R (\frac{g R}{2 V ^{2}} - 1)$

$R / (\frac{2 g R}{V ^{2}} - 1)$

$R (\frac{2 g R}{V ^{2}} - 1)$

$Δ K . E . = Δ U$
$\Rightarrow \frac{1}{2} M V^{2} = G M_{e} M (\frac{1}{R} - \frac{1}{R + h})$ ...(i)
Also $g = \frac{G M _{e}}{R ^{2}}$ ...(ii)
On solving (i) and (ii),
$h = \frac{R}{( \frac{2 g R}{V ^{2}} - 1 )}$

Q. A rocket of mass M is launched vertically from the surface of the earth with an initial speed V. Assuming the radius of the earth to be R and negligible air resistance, the maximum height attained by the rocket above the surface of the earth is

R/(2V2gR​−1)

R(2V2gR​−1)

R/(V22gR​−1)

R(V22gR​−1)