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

Answer:

• Initial Velocity of second ball $\sf (u_1)\:$ = 0
• Mass of the moving ball $\sf (m_1)\:$ = 0.1 kg
• Final Velocity of the first ball $\sf (v_1)\:$ = $\sf - \dfrac{u_1}{3}$
• Let the mass of second ball be $\sf (m_2)\:$

☯ $\underline{\boldsymbol{According\: to \:the\: Question\:now :}}$

$:\implies\sf v_1 =\bigg\lgroup \dfrac{m_1 - m_2}{m_1 + m_2}\bigg\rgroup u_1 + \bigg\lgroup \dfrac{2m_1m_2}{m_1 + m_2}\bigg\rgroup u_2$

$:\implies\sf - \dfrac{u_1}{3} =\bigg\lgroup \dfrac{0.1 - m_2}{0.1 + m_2}\bigg\rgroup u_1 + \bigg\lgroup \dfrac{2m_1m_2}{m_1 + m_2}\bigg\rgroup \times 0$

$:\implies\sf - \dfrac{u_1}{3} =\bigg\lgroup \dfrac{0.1 - m_2}{0.1 + m_2}\bigg\rgroup u_1$

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

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

$:\implies\sf \dfrac{m_2}{0.1} = 2$

$:\implies\underline{ \boxed{\sf m_2 = 0.2 \: kg }}$

$\therefore\underline{\textsf{ Mass of the second ball is \textbf{ 0.2kg}}}.$

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Answer 2

Answer:

for elastic collision between two balls we can say momentum of two balls is conserved

P_{1i} + P_{2i} = P_{1f} + P_{2f}P

1i

+P

2i

=P

1f

+P

2f

now we have

m_1v_{1i} + m_2v_{2i} = m_1v_{1f} + m_2v_{2f}m

1

v

1i

+m

2

v

2i

=m

1

v

1f

+m

2

v

2f

0.1*v_{1i} + m_2*0 = 0.1*(-\frac{v_{1i}}{3}) + m_2v_{2f}0.1∗v

1i

+m

2

∗0=0.1∗(−

3

v

1i

)+m

2

v

2f

\frac{0.4v_{1i}}{3} = m_2v_{2f}

3

0.4v

1i

=m

2

v

2f

also for elastic collision we can say

v_{2f} - v_{1f} = v_{1i} - v_{2i}v

2f

−v

1f

=v

1i

−v

2i

v_{2f} - (-\frac{v_{1i}}{3}) = v_{1i} - 0v

2f

−(−

3

v

1i

)=v

1i

−0

v_{2f} = \frac{2v_{1i}}{3}v

2f

=

3

2v

1i

now from above two equations

\frac{0.4v_{1i}}{3} = m_2* \frac{2v_{1i}}{3}

3

0.4v

1i

=m

2

∗

3

2v

1i

m_2 = 0.2 kgm

2

=0.2kg

so mass of other ball is 0.2 kg