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Question #42009

Difficulty: 8/10 | 🟢 Free

The Question

The radius of a spherical black body is measured as $R = 10.0 \text{ cm}$ using an instrument with a least count of $0.1 \text{ cm}$ . Its total radiated thermal power is measured as $P = 100 \text{ W}$ using a wattmeter with a least count of $2 \text{ W}$ . Assuming the Stefan-Boltzmann constant $\sigma$ is known exactly and the surroundings are at absolute zero, what is the maximum percentage error in the calculated absolute temperature $T$ of the black body?

Options

A.
$1.0\%$
B.
$2.5\%$
C.
$6.0\%$
D.
$10.0\%$

Check Your Answer

Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Variable_Constraint

Develop pure symbolic logic skills by mastering algebraic constraints without relying on numerical data.

Concepts Behind This Question

Least Count and Resolution Limits|Stefan-Boltzmann Power Law

Why This Question Is Tricky

Common Mistakes

This question tests the propagation of instrumental least count errors through a non-linear physical relationship, specifically the Stefan-Boltzmann law.

A common trap is incorrectly applying the power rule for errors—either by multiplying the relative error of power by 4 instead of 1/4 (erroneously assuming $T \propto P^4$ instead of $P \propto T^4$ ), or by failing to correctly weight the error contribution from the squared radius term ( $R^{-1/2}$ leading to a 1/2 multiplier).

It forces students to carefully invert the power law before applying logarithmic differentiation.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Units and Measurements - Class 11 Part 1
Concept	Least Count and Resolution Limits
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free