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Question #42424

Difficulty: 8/10 | 🟢 Free

The Question

A pendulum consists of a uniform solid sphere of mass $M$ and radius $R = L/2$ attached to a massless rigid rod of length $L/2$ . The rod's other end is pivoted at a fixed point $O$ , making the distance from $O$ to the sphere's center of mass equal to $L$ . The pendulum is initially at rest in the vertical position. A horizontal impulse $J$ is applied to the lowest point of the sphere. Assuming the maximum angular deflection $\theta_0$ is small, which of the following expressions gives $\theta_0$ ?

Options

A.
$\frac{3J}{M}\sqrt{\frac{5}{22 g L}}$
B.
$\frac{J}{M}\sqrt{\frac{11}{10 g L}}$
C.
$\frac{J}{M}\sqrt{\frac{1}{g L}}$
D.
$\frac{J}{M}\sqrt{\frac{10}{11 g L}}$

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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

Free Body Diagram Isolation|Impulsive Torque and Angular Momentum|Work-Energy Theorem for Rotation

Why This Question Is Tricky

Common Mistakes

This question tests the student's ability to correctly identify the axis of rotation during an impulsive collision to eliminate unknown reaction forces.

A common trap is assuming the pivot exerts no impulsive force, leading students to incorrectly apply $J = M v_{cm}$ or calculate torque about the center of mass without accounting for the pivot's constraint.

By forcing the use of angular impulse about the pivot ( $L = I\omega$ ) and subsequently applying the work-energy theorem with the small-angle approximation, it strictly separates the non-conservative impulsive regime from the conservative swing phase.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Laws of Motion - Class 11 Part 1
Concept	Free Body Diagram Isolation
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free