At an instant when a particle of mass 80 g has a velocity of 25 m/s in the positive y direction, a 75-g particle has a velocity of 20 m/s in the positive x direction. What is the speed of the center of mass of this two-particle system at this instant?
A) 16 m/s
B) 45 m/s
C) 23 m/s
D) 20 m/s
E) 36 m/s

Question

Quizplus · Accepted Answer

The velocity of the center of mass is calculated using the formula: $ v_{cm} = \frac{m_1v_1 + m_2v_2}{m_1 + m_2} $. Here, $ m_1 = 80 \, \text{g} $, $ v_1 = 25 \, \text{m/s} $, $ m_2 = 75 \, \text{g} $, and $ v_2 = 20 \, \text{m/s} $. The center of mass velocity is the vector sum of the velocities divided by the total mass, resulting in a speed of 16 m/s.

At an Instant When a Particle of Mass 80 G