NEET Physics Question - Uncategorized

Assertion (A): If the product of surface area and density is same for two planets, escape velocities at surface will be same for both planets. Reason (R): For given mass of a planet \( v_e propto R^{-1/2} \)

Both (A) & (R) are true and the (R) is the correct explanation of the (A)

Both (A) & (R) are true but the (R) is not the correct explanation of the (A)

(A) is true but (R) is false

Both (A) and (R) are false

Solution:

Assertion (A) is true. Escape velocity \( v_e = sqrt{frac{2GM}{R}} \). Substitute \( M = rho frac{4}{3} pi R^3 \) to get \( v_e = sqrt{frac{8Gpi R^2 rho}{3}} \). If \( R^2 rho \) is constant (derived from \( Arho \) being constant), then \( v_e \) is constant. Reason (R) is true, as \( v_e = sqrt{frac{2GM}{R}} \) shows \( v_e propto R^{-1/2} \) for constant \( M \). However, (R) does not explain (A), as the conditions are different.

Rankers Physics

Question 14: Escape Velocity and Planet Properties

Solution:

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