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A rocket is launched with velocity $10 \mathrm{~km} / \mathrm{s}$. If radius of earth is $R$, then maximum height attained by it will be
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The correct answer is:
$4 R$
Given,
$\mathrm{v}=10 \mathrm{~km} / \mathrm{s}$
$\mathrm{R}=$ radius of the earth
When a rocket is launched, kinetic energy is converted into potential energy.
At maximum height, potential energy is equal to the kinetic energy.
$\begin{aligned}& \text { P.E }=K \cdot E \\& m g(R+H)=\frac{m v^2}{2} \\& R+H=\frac{v^2}{2 g} \\& R+H=\frac{10 \times 1000 \times 10 \times 1000}{2 \times 10} \\& R+H=5 R\left(\text { as } R=6.5 \times 10^6 \mathrm{~m}\right) \\
& H=4 R\end{aligned}$
$\mathrm{v}=10 \mathrm{~km} / \mathrm{s}$
$\mathrm{R}=$ radius of the earth
When a rocket is launched, kinetic energy is converted into potential energy.
At maximum height, potential energy is equal to the kinetic energy.
$\begin{aligned}& \text { P.E }=K \cdot E \\& m g(R+H)=\frac{m v^2}{2} \\& R+H=\frac{v^2}{2 g} \\& R+H=\frac{10 \times 1000 \times 10 \times 1000}{2 \times 10} \\& R+H=5 R\left(\text { as } R=6.5 \times 10^6 \mathrm{~m}\right) \\
& H=4 R\end{aligned}$
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