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Question #42082

Difficulty: 8/10 | 🟢 Free

The Question

Two identical particles $A$ and $B$ , each of mass $m$ , are connected by a light inextensible string of length $L$ . The system is falling freely under gravity. At a certain instant, the string is horizontal and the velocity of both particles is $v_0$ vertically downwards. At this exact instant, particle $A$ strikes a fixed smooth inclined plane of inclination $\theta$ to the horizontal. The collision of $A$ with the incline is perfectly inelastic in the direction normal to the plane. Mass $B$ is positioned such that the horizontal velocity acquired by $A$ is directed away from $B$ , causing the string to immediately jerk. Determine the loss in total kinetic energy of the system immediately after the impact.

Options

A.
$\frac{m v_0^2 \cos^2\theta}{1+\cos^2\theta}$
B.
$\frac{1}{2} m v_0^2 \cos^2\theta$
C.
$\frac{m v_0^2 \sin^2\theta}{1+\sin^2\theta}$
D.
$\frac{m v_0^2 \cos^2\theta}{2+\cos^2\theta}$

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Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Variable_Constraint

Develop pure symbolic logic skills by mastering algebraic constraints without relying on numerical data.

Concepts Behind This Question

Projectile on Inclined Plane|Recoil and Thrust Forces|Constraint Relations via String Length

Why This Question Is Tricky

Common Mistakes

This question tests the ability to handle simultaneous impulsive constraints (normal collision and string jerk).

A common lethal mistake is assuming the string goes slack, which ignores the horizontal deflection of mass A and leads to the distractor 1/2 m v_0^2 cos^2(theta).

Another trap is incorrectly applying conservation of linear momentum to the two-mass system along the incline; students forget that the internal impulsive tension has a horizontal component that projects onto the incline, meaning the net impulsive force on the system along the incline is not zero.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Motion in a Plane - Class 11 Part 1
Concept	Projectile on Inclined Plane
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free