Science, asked by Charmingdoll, 6 months ago

The body of mass 10kg moving with a velocity of 5 m/s hits a body of 1gm at rest. The velocity of the second body after collision, assuming it to be perfectly elastic is (in m/s)

⚠️ Quality answer needed ⚠️​

Answers

Answered by amazingbuddy
11

\huge {\mathfrak {\purple {Answer  : }}}

Velocity of the second body after collision = 10 m/s

\huge {\mathfrak {\green {Given : }}}

  • Mass of the first body = 10 kg
  • Mass of the second body = 1 gm = 0.001 kg
  • Initial velocity of the first body = 5 m/s
  • Initial velocity of the second body = 0 m/s
  • The collision is perfectly elastic

\huge {\mathfrak {\red{To \: Find : }}}

  • Final velocity of the second body

\huge {\mathfrak {\orange {Solution : }}}

Since this is a one dimensional elastic collision we use the formula,

{\pink{\mathtt{\boxed {v_2=\dfrac{m_2-m_1}{m_1+m_2}\times u_2+\dfrac{2m_1}{m_1+m_2}\times u_1}}}}

where

  • v₂ = final velocity of second body

  • m₂ = mass of second body

  • m₁ = mass of first body

  • u₂ = initial velocity of second body

  • u₁ = initial velocity of first body

Substituting the data we get,

\tt v_2=\dfrac{0.001-10}{10+0.001} \times0+\dfrac{2\times 10}{10+0.001}\times 5

\tt v_2=0+\dfrac{20}{10.001} \times 5

\tt v_2 =\dfrac{100}{10.001}

\tt v_2=9.99\:m/s \approx 10\:m/s

Hence the velocity of the second body after collision is 10 m/s.

Remember :

To find the velocity of the first body after collision in an elastic one dimensional collision we use the formula,

{\blue {\boxed {\mathtt v_1=\dfrac{m_1-m_2}{m_1+m_2}\times u_1+\dfrac{2m_2}{m_1+m_2} \times u_2v}}}

Similar questions