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Question #42345

Difficulty: 8/10 | 🟢 Free

The Question

A simple pendulum consists of a bob of mass $m$ and a light string of measured length $R$ . It is released from rest at a small angular displacement $\theta_0$ . At its lowest point, it undergoes a perfectly elastic head-on collision with a stationary identical bob of mass $m$ , which is suspended by a light string of measured length $L$ . The angle $\theta_0$ is calculated using the measured lengths and set exactly such that the second bob would just complete a vertical circular motion. If the measured lengths $R$ and $L$ have maximum percentage errors of $2\%$ and $4\%$ respectively compared to their actual physical values, and $m$ and $g$ are exact, what is the maximum percentage error in the actual tension $T$ experienced by the second string immediately after the collision? (Assume the small angle approximation is valid).

Options

A.
$5\%$
B.
$6\%$
C.
$0\%$
D.
$10\%$

Check Your Answer

Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Intuition_Breaker

Train your brain to resist "obvious" answers that are designed to deceive your intuition.

Concepts Behind This Question

Vertical Circular Motion|Relative Error Propagation in Powers|Significant Figures in Mixed Operations

Why This Question Is Tricky

Common Mistakes

This question tests the student's ability to distinguish between a calculated set parameter and a fluctuating physical variable during error propagation, embedded within a Work-Energy and VCM context.

A common trap is mechanically propagating the $3\%$ error of the calculated angle $\theta_0$ into the velocity and tension equations, leading to a $10\%$ error.

However, because $\theta_0$ is physically fixed during the experiment, its nominal uncertainty does not compound dynamically; the true error arises solely from the actual lengths deviating from the measured lengths in the centripetal force term.

Furthermore, students often forget that the additive constant $mg$ in the tension equation dilutes the relative error of the centripetal component by a factor of $5/6$ , punishing those who blindly assign the $6\%$ centripetal error to the total tension.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Work, Energy, and Power - Class 11 Part 1
Concept	Vertical Circular Motion
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free