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With reference to various laws and principles of mechanics under physics, consider the following statements:

  1. 1. According to Kepler's second law of planetary motion (law of areal velocities), the line joining a planet to the sun sweeps out equal areas in equal intervals of time, which is primarily based on the principle of conservation of angular momentum.
  2. 2. According to Bernoulli's Theorem, which applies to streamline flow of an ideal fluid, the total energy per unit volume (sum of pressure energy, kinetic energy, and potential energy) of the fluid remains constant as it flows through a tube, and pressure decreases when velocity increases.
  3. 3. 'Moment of Inertia' is the property of an object that opposes any change in its rotational motion, and its value depends solely on the mass of the object, independent of its mass distribution or the position of the axis of rotation.

Which of the above statement(s) is/are completely true?

Detailed Explanation & Solution

Statement 1 is true because Kepler's second law (law of areal velocities) is a direct consequence of the law of conservation of angular momentum.

Statement 2 is true because Bernoulli's theorem is based on the law of conservation of energy, according to which the total energy in a streamline flow remains constant (pressure decreases as velocity increases).

Statement 3 is false because the moment of inertia does not depend solely on the total mass of the object, but also on the distribution of mass relative to the axis of rotation.

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