The maximum and minimum distances of a comet from the Sun are

Question:

The maximum and minimum distances of a comet from the Sun are $1.6 \times 10^{12} \mathrm{~m}$ and $8.0 \times 10^{10} \mathrm{~m}$ respectively. If the speed of the comet at the nearest point is $6 \times 10^{4} \mathrm{~ms}^{-1}$, the speed at the farthest point is :

  1. (1) $1.5 \times 10^{3} \mathrm{~m} / \mathrm{s}$

  2. (2) $6.0 \times 10^{3} \mathrm{~m} / \mathrm{s}$

  3. (3) $3.0 \times 10^{3} \mathrm{~m} / \mathrm{s}$

  4. (4) $4.5 \times 10^{3} \mathrm{~m} / \mathrm{s}$


Correct Option: 3

Solution:

(3)

By angular momentum conservation :

$\mathrm{mv}_{1} \mathrm{r}_{1}=\mathrm{mv}_{2} \mathrm{r}_{2}$

$\mathrm{v}_{1}=\frac{48 \times 10^{14}}{1.6 \times 10^{12}}=3000 \mathrm{~m} / \mathrm{sec}$

$=3 \times 10^{3} \mathrm{~m} / \mathrm{sec}$

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