First slide

Dimensions of physical quantities

Question

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

Moderate

A

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

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

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

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

Solution

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

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