In a direct impact, loss in kinetic energy is given by Δ K=(M1M2/2(M1+M2)).(V1-V2)2 (1-K2) with usual notations (except k). The quantity k will have dimensional formula

Question

In a direct impact, loss in kinetic energy is given by Δ K=(M1M2/2(M1+M2)).(V1-V2)2 (1-K2) with usual notations (except k). The quantity k will have dimensional formula (A) [M0L2T-2] (B) [MLT-1] (C) [M0L0T0] (D) [M0LT-1]

Tardigrade Admin · Accepted Answer

It is clear that k should be dimensionless [1- k2] =M0L0T0 Hence, [K] = M0 L0 T0 Actually k is the coefficient of restitution.

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

$[M^{0} L^{2} T^{- 2}]$

$[M L T^{- 1}]$

$[M^{0} L^{0} T^{0}]$

$[M^{0} L T^{- 1}]$

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.

Q. In a direct impact, loss in kinetic energy is given by ΔK=2(M1​+M2​)M1​M2​​.(V1​−V2​)2(1−K2) with usual notations (except k). The quantity k will have dimensional formula

[M0L2T−2]

[MLT−1]

[M0L0T0]

[M0LT−1]