Ques. 1JEE Main 2024, 5 April (Morning Shift)
Match List I with List II : (Where a = radius of planet orbit, r = radius of planet, M = mass of Sun, m = mass of planet) Choose the correct answer from the options given below :
- (A)-(II), (B)-(I), (C)-(IV), (D)-(III)
- (A)-(I), (B)-(II), (C)-(III), (D)-(IV)
- (A)-(III), (B)-(IV), (C)-(I), (D)-(II)
- (A)-(I), (B)-(IV), (C)-(II), (D)-(III)
Answer
(1) (A)-(II), (B)-(I), (C)-(IV), (D)-(III)
Solution
mv2a = GMma2 (gravity gives the centripetal force)
(A): K = 12mv2 = GMm2a ⇒ (A) is (II)
(B): U = - GMma ⇒ (B) is (I)
(C): E = K + U = - GMm2a ⇒ (C) is (IV)
(D): escape energy for unit mass = -Usurface = Gmr ⇒ (D) is (III)
Answer: (1)