First slide

Types of collision

Question

Two steel spheres approach each other headon with the same speed and collide elastically. After the collision one of the sphere's of radius r comes to rest. The radius of the other sphere is

Difficult

A

$\large \frac {r}{(3)^{1/3}}$
B

$\large \frac r3$
C

$\large \frac r9$
D

$\large (3)^{1/2}r$

Solution

v₂ = 0

$\large \frac{{2{m_1}{u_1}}}{{{m_1} + {m_2}}} - \left( {\frac{{{m_2} - {m_1}}}{{{m_1} + {m_2}}}} \right){u_2} = 0$
$\large \frac{{2{m_1}v}}{{{m_1} + {m_2}}} = \left( {\frac{{{m_2} - {m_1}}}{{{m_1} + {m_2}}}} \right)v\$
$\large 3{m_1} = {m_2} \Rightarrow {m_1} = \frac{{{m_2}}}{3}$

Alternative Method:
m₁v₁ + m₂ x 0 = m₁u + m₂(-u)
⇒ m₁v₁ = (m₁ - m₂)u.........(1)

$\large \frac {0-v_1}{+u-(-u)}=e=1\Rightarrow v_1=-2u...(2)$

From (1) and (2), 3m₁ = m₂

$\large \therefore 3\left ( \frac 43\pi R^3\rho \right )=\frac 43\pi r^3.\rho\Rightarrow R=\frac {r}{(3)^{1/3}}$

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