Question

Kepler's second law states that the straight line joining the planet to the sun sweeps out equal areas at equal times. This statement is equivalent to saying that

• A. Total acceleration is zero
• B. Tangential acceleration is zero
• C. Longitudinal acceleration is zero
• D. Radial acceleration is zero

Answer 1

The correct option is B

Tangential acceleration is zero

The explanation for the correct option:

In the case of option B,

1. Earth and all other planets move around the sun under the influence of gravitational force.
2. This force always acts along the line connecting the center of the planet and the sun and is directed towards the sun.
3. A planet moves around the sun under the influence of radial force.
4. Therefore, areal velocity of the planet must always remain constant.

$\frac{∆\overrightarrow{A}}{∆t}=\frac{\overrightarrow{L}}{2m}=$a constant vector

Therefore, Kepler's 2nd law is the consequence of the principle of conservation of angular momentum $\left(L\right)$

$\tau =\frac{dl}{dt}=0$ (where $\tau =$Torque, $I=$Moment of inertia, $\alpha =$Angular acceleration)

Now, $\tau =I\alpha$

$\therefore I\alpha =0$ or $\alpha =0$

or $aT=r\alpha =0$

Hence, option B is the correct answer.