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Question #42289

Difficulty: 8/10 | 🟢 Free

The Question

A uniform spherical planet of mass $M$ and initial radius $R$ rotates about its axis with an initial angular velocity $\omega$ . The coefficient of linear thermal expansion of the planet's material is $\alpha$ . The planet undergoes a uniform temperature increase of $\Delta T$ . Assuming no external torques act on the planet and $\alpha \Delta T \ll 1$ , what is the approximate change in the effective acceleration due to gravity ( $\Delta g_{eff}$ ) at the planet's equator? Let $g = \frac{GM}{R^2}$ be the initial true acceleration due to gravity at the surface.

Options

A.
$\alpha \Delta T (3\omega^2 R - 2g)$
B.
$-\alpha \Delta T (2g + \omega^2 R)$
C.
$\alpha \Delta T (\omega^2 R - 2g)$
D.
$-\alpha \Delta T (2g - \omega^2 R)$

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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

Effect of Earth's Rotation on g|Variation of Density with Temperature|Integration

Why This Question Is Tricky

Common Mistakes

This question tests the coupling of thermal expansion, non-inertial reference frames, and conservation of angular momentum.

The primary trap is treating the planet's angular velocity $\omega$ as a constant during thermal expansion.

Students often correctly adjust the radius in the gravitational term and the centrifugal term but fail to realize that an expanding planet increases its moment of inertia.

Without external torques, angular momentum is conserved, forcing $\omega$ to decrease.

This creates a counter-intuitive feedback loop where the centrifugal acceleration actually decreases (proportional to $R^{-3}$ ) rather than increases (proportional to $R$ ), fundamentally altering the variation in effective gravity.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Gravitation - Class 11 Part 1
Concept	Effect of Earth's Rotation on g
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free