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Physics · GRAVITATION

हिन्दी

Given below are statements regarding planetary motion: (A) Kepler's second law (law of areas) is a direct consequence of the conservation of angular momentum. (B) The linear speed of a planet is maximum when it is at perihelion. (C) A central force exerts zero torque about the centre of force. (D) For any planet, the ratio \( T^2 / a^3 \) depends strongly on the planet's mass \( m \). Choose the correct answer from the options given below:

  1. (A) and (D) only
  2. (B) and (D) only
  3. (A), (B) and (C) only
  4. (A), (B), (C) and (D)

Correct answer · Option 3

(A), (B) and (C) only

Explanation

(A), (B), and (C) are correct. (D) is incorrect because \( T^2/a^3 \) is a universal constant for all planets revolving around the same Sun, independent of planet mass \( m \ll M_S \).

Related questions

Consider the following statements regarding the energies of an Earth satellite in a circular orbit of radius \( r \) (\( r = R_E + h \)): (A) Kinetic energy \( K.E. = \frac{G M_E m}{2r} \) (B) Potential energy \( P.E. = -\frac{G M_E m}{r} \) (C) Total energy \( E = -\frac{G M_E m}{2r} \) (D) \( K.E. = -2E \) Which of the above statements are correct?→The gravitational force between two point masses \( m_1 \) and \( m_2 \) separated by distance \( r \) is \( F \). If the mass \( m_1 \) is increased by \( 100\% \), mass \( m_2 \) is decreased by \( 50\% \), and the distance between them is halved, the new gravitational force will be:→In the given diagram, a point mass \( m \) is located at depth \( d \) from the Earth's surface. What fraction of the Earth's total mass \( M_E \) contributes to the gravitational force acting on this mass, assuming uniform density?→The work done in lifting a particle of mass \( m \) from a distance \( r_1 \) to \( r_2 \) (where \( r_2 > r_1 > R_E \)) from the centre of the Earth of mass \( M_E \) is:→
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