Question

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

• A. $1.5\times {10}^3\text{m/s}$
• B. $4.5\times {10}^3\text{m/s}$
• C. $3.0\times {10}^3\text{m/s}$
• D. $6.0\times {10}^3\text{m/s}$

Answer 1

The correct option is C $3.0\times {10}^3\text{m/s}$


Let point 1 be the nearest point, and point 2 be the farthest point.

Given, $r_1=8\times {10}^{10}\text{m}$ & $r_2=1.6\times {10}^{12}\text{m}$

Using angular momentum conservation,
$L_1=L_2$
$m{r}_1{v}_1=m{r}_2{v}_2$
$\Rightarrow v_2=\frac{r_1{v}_1}{r_2}$
$\therefore v_2=\frac{8\times {10}^{10}\times 6\times {10}^4}{1.6\times {10}^{12}}$
$=3.0\times {10}^3\text{m/s}$
Hence option (c) is correct.