Question

A 4.38 kg sphere makes a perfectly inelastic collision with a second sphere that is initially at rest. The composite system moves with a speed equal to one third the original speed of the 4.38 kg sphere. What is the mass of the second sphere?

Answer 1

Answer: The mass of the second sphere is 8.76 kg

Explanation:

The equation for a perfectly inelastic collision follows:

$m_1u_1+m_2u_2=(m_1+m_2)v$

where,

$m_1\text{ and }u_1$ are the mass and initial velocity of first sphere

$m_2\text{ and }u_2$ are the mass and initial velocity of second sphere

v = final velocity of the system

We are given:

$m_1=4.38kg\\u_2=0m/s\\v=\frac{u_1}{3}$

Rearranging the above equation, we get:

$m_1u_1-m_1v=m_2v\\\\m_2=m_1\frac{u_1-v}{v}\\\\m_2=m_1(\frac{u_1}{v}-1)$

Plugging values in the above equation, we get:

$m_2=4.38(\frac{3u_1}{u_1}-1)\\\\m_2=(4.38\times 2)=8.76kg$

Hence, the mass of the second sphere is 8.76 kg