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PhysicsMultiple correct+3Question 67 of 84

IIT-JEE 2010 · Paper 1, Physics question 67

A point mass of 1 kg collides elastically with a stationary point mass of 5 kg. After their collision, the 1 kg mass reverses its direction and moves with a speed of 2 m s⁻¹. Which of the following statement(s) is (are) correct for the system of these two masses?

Choose one or more options
Answer and worked solution

Official answer: A, C

Initial speed. In an elastic head-on collision with a stationary target,
v1′=m1−m2m1+m2u=−23u=−2  ⟹  u=3 m s−1.v_1'=\frac{m_1-m_2}{m_1+m_2}u=-\frac23u=-2\implies u=3\text{ m s}^{-1}.
The 5 kg mass moves off with v2′=2m1m1+m2u=1v_2'=\frac{2m_1}{m_1+m_2}u=1 m s⁻¹.

  • (A) Total momentum 1×3=31\times3=3 kg m s⁻¹. True.
  • (B) The 5 kg mass has momentum 5 kg m s⁻¹. False.
  • (C) Kcm=p22M=912=0.75K_\text{cm}=\dfrac{p^2}{2M}=\dfrac9{12}=0.75 J. True.
  • (D) Total KE =12×1×32=4.5=\frac12\times1\times3^2=4.5 J. False.

(A), (C)

Topics:Elastic and inelastic collisionsCentre of mass
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