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Question #42429

Difficulty: 8/10 | 🟢 Free

The Question

Two particles $A$ and $B$ of masses $m$ and $2m$ respectively lie on a smooth horizontal $xy$ -plane. They are connected by a light inextensible string of length $L$ . Initially, particle $A$ is at rest at the origin $(0,0)$ and particle $B$ is at rest at $(\frac{3L}{5}, 0)$ . Particle $B$ is suddenly projected with a velocity $v_0 \hat{j}$ along the positive $y$ -direction while $A$ remains free to move. What is the magnitude of the velocity of particle $A$ just after the string becomes taut?

Options

A.
$\frac{8v_0}{15}$
B.
$\frac{4v_0}{15}$
C.
$\frac{2v_0}{5}$
D.
$\frac{2v_0}{3}$

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

Constraint Relations via String Length|Collision Impulses|System vs Particle Displacement

Why This Question Is Tricky

Common Mistakes

This question tests the understanding of constraint relations coupled with collision impulses.

Students often incorrectly assume the jerk acts like a perfectly inelastic collision in all directions, leading them to conserve total vector momentum and find a common final velocity vector $\vec{v} = \frac{2}{3}v_0 \hat{j}$ .

The physical trap lies in failing to recognize that the impulsive tension is a directional internal force acting only along the string's axis.

Therefore, momentum is only conserved as a scalar sum along the string's axis to satisfy the geometric velocity constraint ( $v_{An} = v_{Bn}$ ), while the perpendicular velocity component of the projected mass remains unaffected by the jerk.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Laws of Motion - Class 11 Part 1
Concept	Constraint Relations via String Length
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free