The maximum and minimum distances
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 afthe nearest point is $6 \times 10^{4} \mathrm{~ms}^{-1}$, the speed at the farthest point is:

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

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

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

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

Correct Option: , 3

Solution:

By angular momentum conservation :

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

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

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