Question

Every planet revolves around the sun in an elliptical orbit:-
A. The force acting on a planet is inversely proportional to square of distance from sun
B. Force acting on planet is inversely proportional to product of the masses of the planet and the sun
C. The Centripetal force acting on the planet is directed away from the sun
D. The square of time period of revolution of planet around sun is directly proportional to cube of semi-major axis of elliptical orbit
Choose the correct answer from the options given below:

• A. A and D only
• B. $B$ and $C$ only
• C. $A$ and $C$ Only
• D. C and Donly

Answer 1

The Correct Option is A

The correct answer is (A) : A and D only
$F=\frac{G{m}_1{m}_2}{r^2}$
$\Rightarrow F\propto \frac{1}{r^2}$
$\Rightarrow F\propto m_1{m}_2$
$\Rightarrow$ This force provides centripetal force and acts towards sun
$\Rightarrow T^2\propto a^3\text{(Kepler’s third law)}$

Answer 2

Statement A is correct, as it accurately reflects Newton's law of universal gravitation, which states that the gravitational force between two masses is inversely proportional to the square of the distance between them.
Statement D is correct, as it expresses Kepler's third law, which links the square of a planet's orbital period to the cube of its semi-major axis in elliptical orbits.
Statement B is incorrect because the gravitational force is directly proportional to the product of the masses, not inversely.
Statement C is incorrect because the centripetal force always points towards the center of motion (the sun), not away from it.