Question

Two spheres are moving towards each other. Both have same radius but their masses are 2 kg and 4 kg. If the velocities are 4 m/s and 2 m/s respectively and coefficient of restitution is e = 1/3, find the maximum potential energy of deformation.

• A. 36 J
• B. 18 J
• C. 20 J
• D. 15 J

Answer 1

The correct option is B 18 J

Answer is B.
Maximum potential energy of deformation is equal to loss in kinetic energy during deformation upto maximum deformed state,
$U=\frac{1}{2}{m}_1(u_{1}cos\theta {)}^2+\frac{1}{2}{m}_2(u_{2}cos\theta {)}^2-\frac{1}{2}(m_1+m_2)v^2$
$=\frac{1}{2}2(4cos{30}^{\circ }{)}^2+\frac{1}{2}4(-2cos{30}^{\circ }{)}^2-\frac{1}{2}(2+4)(0{)}^2$ or U = 18 Joule.
Hence, the maximum potential energy of deformation is 18 J.