Question

The maximum and minimum distances of a comet from the Sun are $8 \times 10^{12} \, \text{m}$ and $1.6 \times 10^{12} \, \text{m}$. If its velocity when nearest to the Sun is $60 \, \text{m/s}$, what will be its velocity in m/s when it is farthest?

• A. 12
• B. 6
• C. 112
• D. 60

Hint:

The velocity of a comet is inversely proportional to the distance from the Sun when it follows an elliptical orbit.

Answer 1

The Correct Option is A

The velocity of a comet follows the law of conservation of angular momentum: \[ m v_1 r_1 = m v_2 r_2 \] where: $m$ is the mass of the comet, $v_1$ and $v_2$ are the velocities at the nearest and farthest points, and $r_1$ and $r_2$ are the corresponding distances. Using the given values: \[ v_2 = \frac{v_1 r_1}{r_2} = \frac{60 \times 8 \times 10^{12}}{1.6 \times 10^{12}} = 12 \, \text{m/s} \]