Physics And Measurement Question 191
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
Options:
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} $ ]
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Answer:
Correct Answer: C
Solution:
[c] It is clear that k should be dimensionaless
$ [1-k^{2}]=M^{0}L^{0}T^{0} $
Hence, [k]= $ M^{0}L^{0}T^{0} $
Actually k is the coefficient of restitution,
