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Question #43525

Difficulty: 8/10 | 🟢 Free

The Question

A uniform cylindrical rod of length $L$ , cross-sectional area $A$ , density $\rho$ , Young's modulus $Y$ , and coefficient of linear thermal expansion $\alpha$ is rigidly secured between two vertical supports. These supports are fixed to a horizontal platform. Initially, the system is at rest and the rod is unstressed. The platform then begins to move along the longitudinal axis of the rod with a constant acceleration $a$ . Simultaneously, the temperature of the rod is uniformly increased by $\Delta T$ . Assuming the supports are perfectly rigid and the rod does not buckle, what is the magnitude of the compressive stress in the rod at its rear end (the end opposite to the direction of acceleration)?

Options

A.
$Y \alpha \Delta T + \frac{1}{2} \rho L a$
B.
$Y \alpha \Delta T + \rho L a$
C.
$Y \alpha \Delta T - \frac{1}{2} \rho L a$
D.
$Y \alpha \Delta T$

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

Frame of Reference Dependency|Thermal Stress in Constrained Rods|Thermal Expansion of Area and Volume

Why This Question Is Tricky

Common Mistakes

This question tests the student's ability to superimpose intrinsic thermal strain with dynamic stress in a non-inertial frame.

A common trap is assuming that the entire inertial load is borne by the rear support (leading to the incorrect term $\rho L a$ ) or ignoring the pseudo-force entirely because thermal expansion is often treated as a purely static phenomenon.

Students must recognize that the geometric constraint of fixed ends forces the inertial load to be distributed symmetrically relative to the center of mass, modifying the uniform thermal stress by exactly $\pm \frac{1}{2}\rho L a$ at the boundaries.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Motion in a Straight Line - Class 11 Part 1
Concept	Frame of Reference Dependency
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free