Question

a moving ball of mass 0.1 kg undergoes an Elastic head on collision with another ball at rest after frozen the first body was at one third of its origin speed while the second wall stars moving forward find the mass of the second wall .​

Answer 1

ㅤ$\;\;\underline{\textbf{\textsf{Given: -}}}$

• Mass of moving ball, $\sf{m_1=0.1\ kg}$

• Initial velocity of second ball is = $\sf{u_2=0}$

•Final velocity of first ball is, $\sf{v_1=-\dfrac{u_1}{3}.}$

ㅤ$\;\;\underline{\textbf{\textsf{To Find: -}}}$

• Mass of second ball

ㅤ$\;\;\underline{\textbf{\textsf{Solution : -}}}$

$\underline{\:\textsf{ We know that :}}$

$\sf{\dashrightarrow v_1=\left(\dfrac{m_1-m_2}{m_1+m_2}\right)u_1+\left(\dfrac{2m_1m_2}{m_1+m_2}\right)u_2}$

$\underline{\:\textsf{ Putting the given values :}}$

$\sf{ \dashrightarrow -\dfrac{u_1}{3}=\left(\dfrac{0.1-m_2}{0.1+m_2}\right)u_1+\left(\dfrac{2m_1m_2}{m_1+m_2}\right)(0)}$

$\sf{\dashrightarrow -\dfrac{u_1}{3}=\left(\dfrac{0.1-m_2}{0.1+m_2}\right)u_1}$

$\sf{\dashrightarrow \dfrac{0.1-m_2}{0.1+m_2}=\dfrac{-1}{3}}$

$\sf{\dashrightarrow \dfrac{m_2}{0.1}=\dfrac{3-(-1)}{3+(-1)}}$

$\sf{\dashrightarrow \dfrac{m_2}{0.1}=2}$

$\dashrightarrow {\boxed{\frak{\purple{m_2 = 0.2\;kg}}}}$

ㅤ$\;\;\underline{\textbf{\textsf{Hence -}}}$

$\underline{\textsf{ Mass of the second ball is</p><p>\textbf{ 0.2kg}}}.$

━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━