Question

Arrange the following in ascending order of their escape speeds :
A. Jupiter
B. Sun
C. Earth
D. Neutron Star

• A. \(A < B < C < D \)
• B. \(C < B < A < D \)
• C. \(A < C < B < D \)
• D. \(C < A < B < D \)

Hint:

Escape velocity is a measure of "gravitational grip." Planets < Stars < Compact objects (White Dwarfs, Neutron Stars) < Black Holes.

Answer 1

The Correct Option is D

Concept: The escape speed ($v_e$) of a celestial body depends on its mass ($M$) and radius ($R$), given by the formula: \[ v_e = \sqrt{\frac{2GM}{R}} \] Generally, more massive and denser objects have significantly higher escape speeds.

Step 1: Compare the masses and radii of the given bodies.

• Earth (C): Smallest mass among the list ($v_e \approx 11.2 \text{ km/s}$).
• Jupiter (A): Largest planet, much more massive than Earth ($v_e \approx 59.5 \text{ km/s}$).
• Sun (B): A star, containing 99.8% of the solar system's mass ($v_e \approx 615 \text{ km/s}$).
• Neutron Star (D): Extremely dense remnant of a star; mass comparable to the Sun but radius of only ~10 km ($v_e$ can be up to $0.7c$, approx $2 \times 10^5 \text{ km/s}$).

Step 2: Arrange in ascending order.
Comparing the values: Earth < Jupiter < Sun < Neutron Star. This corresponds to: \(C < A < B < D\).