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Question #42002

Difficulty: 8/10 | 🟢 Free

The Question

Satellite $S_1$ orbits a planet at a radial distance $R = 6.4 \times 10^3 \text{ km}$ from its center. Satellite $S_2$ orbits the same planet at a radial distance $R + h$ , where $h = 1.4 \text{ km}$ . According to Kepler's Third Law, calculate the percentage increase in the orbital period of $S_2$ relative to $S_1$ , i.e., $\frac{T_2 - T_1}{T_1} \times 100$ . Express your final answer with the correct number of significant figures.

Options

A.
$0.033 \%$
B.
$0.0328 \%$
C.
$0.03281 \%$
D.
$0.03 \%$

Check Your Answer

Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Multi-Concept_Bridge

Master problems that require linking physics and math concepts to solve complex competitive questions.

Concepts Behind This Question

Significant Figures in Mixed Operations|Kepler’s Third Law (Time Period)|Gravitational Field Variation (Depth vs Height)

Why This Question Is Tricky

Common Mistakes

This question tests the synthesis of Kepler's Third Law, the binomial approximation for small variations in gravitational fields, and the propagation of significant figures.

A common trap is treating the calculated percentage ( $0.0328125 \%$ ) as an exact value or arbitrarily rounding it to standard decimal places (e.g., $0.0328 \%$ ).

Students must recognize that the binomial expansion $(1+x)^n \approx 1+nx$ is a physical approximation constrained by the precision of the measured inputs.

Since both $h$ and $R$ are provided with two significant figures, the final result must be strictly truncated to two significant figures, penalizing the retention of 'ghost precision'.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Units and Measurements - Class 11 Part 1
Concept	Significant Figures in Mixed Operations
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free