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A planet moving along an elliptical orbit is closest to the sun at a distance of $r_{1}$ and farthest away at a distance of r₂. If $V_{1}$ and $V_{2}$ are the linear velocities at these points respectively, then the ratio $\frac{V_{1}}{V_{2}}$ is

Option 1)
$(r_{1}/r_{2})^{2}$

Option 2)
$r_{2}/r_{1}$

Option 3)
$(r_{2}/ r_{1})^{2}$

Option 4)
$r_{1}/r_{2}$

Answers (1)

As we discussed in concept ID

Angular momentum of satellite -

$L=mvr$

$L=sqrt{m^{2}GMr}$

$L=$ Angular momentum

$m ightarrow$ mass of satellite

- wherein

$v$ depends on both the masses , mass of centre of body and mass of planet as well as radius of earth.

According to conservation of Angular momentum

$L_{1}=L_{2}$

$mv_{1}r_{1}=mv_{2}r_{2}$

$v_{1}r_{1}=v_{2}r_{2}$

$\frac{v_{1}}{v_{2}}=\frac{r_{2}}{r_{1}}$

Option 1)

$(r_{1}/r_{2})^{2}$

Incorrect Option

Option 2)

$r_{2}/r_{1}$

Correct Option

Option 3)

$(r_{2}/ r_{1})^{2}$

Incorrect Option

Option 4)

$r_{1}/r_{2}$

Incorrect Option

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subam

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