JEE Main · 2024 · 05 Apr 2024 · Shift 1 · Gravitation

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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:

Answer: A → II, B → I, C → IV, D → III

Solution

For a planet in orbit of radius

a

: kinetic energy

KE = \frac{GM m}{2 a}

(matches II); gravitational potential energy of the Sun-planet system

U = - \frac{GM m}{a}

(matches I); total mechanical energy

E = KE + U = - \frac{GM m}{2 a}

(matches IV); escape energy per unit mass at the planet surface

= \frac{G m}{r}

(matches III). Correct matching: A-II, B-I, C-IV, D-III. Allen's key is (A)-II, (B)-I, (C)-IV, (D)-III, i.e. pairs

[[0, 1], [1, 0], [2, 3], [3, 2]]

JEE Main · 2024 · 05 Apr 2024 · Shift 1 · Match the columns

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