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Chapter 6: Problem 58

Two identical particles move towards each other with velocity \(2 v\) and \(v\), respectively. The velocity of the centre of mass is (A) \(v\) (B) \(\frac{v}{3}\) (C) \(\frac{v}{2}\) (D) Zero

Short Answer

Expert verified
The velocity of the center of mass is \(\frac{v}{2}\) (Option C).

Step by step solution

01

Identify particles' mass and velocity

Let m1 and m2 be the masses of the two particles, and v1 and v2 be their respective velocities. Since the particles are identical, their masses are the same (m1=m2=m). Given: v1 = 2v v2 = -v (negative sign because both particles are moving towards each other)
02

Use the formula for the center of mass velocity

The formula for the velocity of the center of mass is given by: COM_velocity = \(\frac{m_1v_1 + m_2v_2}{m_1 + m_2}\) Here, we can substitute the values of m1, m2, v1, and v2. COM_velocity = \(\frac{m(2v) + m(-v)}{m + m}\)
03

Simplify and solve for the COM_velocity

Simplify the expression for the COM_velocity: COM_velocity = \(\frac{m(2v - v)}{2m}\) COM_velocity = \(\frac{m(v)}{2m}\) The mass m will cancel out: COM_velocity = \(\frac{v}{2}\) Hence, the correct answer is: (C) \(\frac{v}{2}\)

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