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Question #76821

Difficulty: 5/10 | 🟢 Free

The Question

A small block of mass $M$ is constrained to move along a smooth horizontal rail. A uniform rod, also of mass $M$ and length $L$ , is hinged to the block at its upper end and initially hangs vertically at rest. A horizontal impulse $J$ is applied to the lower end of the rod. Find the minimum value of $J$ required for the rod to swing and momentarily reach a horizontal position. (Acceleration due to gravity is $g$ )

Options

A.
$M \sqrt{\frac{10 g L}{27}}$
B.
$M \sqrt{\frac{g L}{3}}$
C.
$M \sqrt{\frac{25 g L}{108}}$
D.
$M \sqrt{\frac{25 g L}{76}}$

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

Potential Energy Reference|Impulsive Torque and Angular Momentum|Variable Force Integration

Why This Question Is Tricky

Examiner Levers

Dimensional Analysis

Tests if the student verifies units/dimensions before selecting.

Difficulty Boost : +2

Common Mistakes

This question tests the student's ability to handle impulsive torques about an accelerating pivot and decouple energy frames.

A common trap is incorrectly applying $L = I\omega$ about the moving hinge ( $JL = \frac{ML^2}{3}\omega$ ), ignoring that the hinge is neither fixed nor the center of mass, meaning its sudden acceleration generates a pseudo-torque during the impulsive phase.

Furthermore, it tests the strategic use of the Work-Energy theorem: applying it in the ground frame is mathematically bloated, but shifting to the inertial Center of Mass frame elegantly isolates the convertible kinetic energy $K_{cm}$ from the conserved translational kinetic energy of the system.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Work, Energy, and Power - Class 11 Part 1
Concept	Potential Energy Reference
Difficulty	5
Cognitive Load	6
Target Solve Time	140 sec
Access	Free