NEETPhysicsGravitation
Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A): If the distance of the Earth from the Sun were suddenly reduced to half its present value, the number of days in a year would become approximately 129 . Reason (R): The time period of revolution of a planet is directly proportional to the cube of the semi-major axis of its elliptical orbit. In the
Options
- ABoth (A) and (R) are true and (R) is the correct explanation of (A)
- BBoth (A) and (R) are true but (R) is not the correct explanation of (A)
- C(A) is true but (R) is false
- D(A) is false but (R) is true
Correct answer
C. (A) is true but (R) is false
Step-by-step solution
Assertion (A) is true: Let the initial distance be r ₁ = r and initial time period be T ₁ = 365 days. If the distance is reduced to half, r ₂ = r 2 . According to Kepler's third law, T ^2 r ^3 . ( T ₂ T ₁ )^2 = ( r ₂ r ₁ )^3 T ₂ 365 = ( 1 2 )^ 3/2 = 1 2 2 T ₂ = 365 2 1.414 365 2.828 129 days. Reason (R) is false: Kepler's third law states that the square of the time period of revolution ( T ^2 ) is directly proportional to the cube of the semi-major axis ( r ^3 ), not the time period itself. Therefore, (A) is true