Question

In a direct impact, loss in kinetic energy is given by
$\Delta K=\frac{M_{1}M_{2}}{2(M_{1}+M_{2})}.(V_{1}-V_{2})^{2} (1-K^{2})$
with usual notations (except $k$). The quantity k will have dimensional formula

• A. $[M^{0}L^{2}T^{-2}]$
• B. $[MLT^{-1}]$
• C. $[M^{0}L^{0}T^{0}]$
• D. $[M^{0}LT^{-1}]$

Answer 1

Answer: (C)

It is clear that $k$ should be dimensionless
$[1- k^{2}] =M^{0}L^{0}T^{0}$
Hence, $[K] = M^{0} L^{0} T^{0}$
Actually $k$ is the coefficient of restitution.