SATHEE: Physics And Measurement Question 191

Physics And Measurement Question 191

Question: 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

Options:

A) [ $M_{}^{0} L_{}^{2} T_{}^{- 2}$ ]

B) [ $M_{}^{} L_{}^{} T_{}^{- 1}$ ]

C) [ $M_{}^{0} L_{}^{0} T_{}^{0}$ ]

D) [ $M_{}^{0} L_{}^{} T_{}^{- 1}$ ]

Show Answer

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,

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Physics And Measurement Question 191

Question: In a direct impact, loss in kinetic energy is given by ΔK=M1M22(M1+M2).(V1−V2)2(1−k2) with usual notations (except k). The quantity k will have dimensional formula

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Answer:

Solution:

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Question: 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