Question:

Particle $A$ makes a perfectly elastic collision with another particle $B$ at rest. They fly apart in opposite directions with equal speeds. The ratio of their masses $m_A/m_B$ is

Updated On: Jul 28, 2022
  • 44563
  • 44564
  • 44565
  • $1 / \sqrt{3}$
Hide Solution
collegedunia
Verified By Collegedunia

The Correct Option is B

Solution and Explanation

According to law of conservation of linear momentum, we get $m_1 u_1 + m_2 \times 0 = m_1 v_1 + m_2 (-v_1)$ $m_1 u_1 = (m_1 - m_2) v_1$ .....(i) $\therefore \:\: \frac{u_1}{v_1} = \frac{m_1 - m_2}{m_1}$ ....(ii) According to law of conservation of kinetic energy, we get $\frac{1}{2} m_1 u_1^2 = \frac{1}{2} (m_1 + m_2)v_1^2$ ...(iii) Divide (iii) by (i), we get $u_{1}=\frac{\left(m_{1}+m_{2}\right)v_{1}}{m_{1}-m_{2}} $ or $\frac{u_{1}}{v_{1}}=\frac{m_{1}+m_{2}}{m_{1}-m_{2}}$ ...(iv) From (ii) and (iv), we get $\frac{m_{1}-m_{2}}{m_{1}}=\frac{m_{1}+m_{2}}{m_{1}-m_{2}}$ On solving, we get $\frac{m_1}{m_2} = \frac{1}{3}$ or $\frac{m_A}{m_B} = \frac{1}{3}$
Was this answer helpful?
0
0

Concepts Used:

Collision Theory

The collision theory states that a chemical reaction can only occur between particles when they collide (hit each other). The collision between reactant particles is necessary but not sufficient for a reaction to take place. The collisions also have to be effective. It is important to understand the exact nature of an effective collision since this determines whether particles react with each other and form new products.

Molecular Collisions

  • The more molecules are present, the more collisions will happen.
  • Molecules must collide before they can react.
  • To effectively initiate a reaction, collisions must be sufficiently energetic
    (kinetic energy) to bring about this bond disruption.
  • As the temperature rises, molecules move faster and collide more vigorously,
    greatly increasing the likelihood of bond cleavages and rearrangements.
  • Most reactions involving neutral molecules cannot take place at all until they have acquired the activation energy needed to stretch, bend, or otherwise distort one or more bonds.