The SI Unit Of Energy Is J Kg M2 S2 That Of Speed V Class 11 ... - Vedantu

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• The SI unit of energy is J kg ...

AnswerQuestion Answers for Class 12Class 12 BiologyClass 12 ChemistryClass 12 EnglishClass 12 MathsClass 12 PhysicsClass 12 Social ScienceClass 12 Business StudiesClass 12 EconomicsQuestion Answers for Class 11Class 11 EconomicsClass 11 Computer ScienceClass 11 BiologyClass 11 ChemistryClass 11 EnglishClass 11 MathsClass 11 PhysicsClass 11 Social ScienceClass 11 AccountancyClass 11 Business StudiesQuestion Answers for Class 10Class 10 ScienceClass 10 EnglishClass 10 MathsClass 10 Social ScienceClass 10 General KnowledgeQuestion Answers for Class 9Class 9 General KnowledgeClass 9 ScienceClass 9 EnglishClass 9 MathsClass 9 Social ScienceQuestion Answers for Class 8Class 8 ScienceClass 8 EnglishClass 8 MathsClass 8 Social ScienceQuestion Answers for Class 7Class 7 ScienceClass 7 EnglishClass 7 MathsClass 7 Social ScienceQuestion Answers for Class 6Class 6 ScienceClass 6 EnglishClass 6 MathsClass 6 Social ScienceQuestion Answers for Class 5Class 5 ScienceClass 5 EnglishClass 5 MathsClass 5 Social ScienceQuestion Answers for Class 4Class 4 ScienceClass 4 EnglishClass 4 MathsThe SI unit of energy is $J= kg m^2 s^{-2}$; that of speed v is $ms^{-1}$ and of acceleration is $ms^{-2}$. Which of the formula for kinetic energy (K) given below can you rule out on the basis of dimensional arguments (m stands for mass of the body):(The question has multiple correct options)A. $K=m^2 v^3$B. $K= (1/2) mv^2$C. $K=ma$D. $K=(3/16) m v^2$E. $K= (1/2) mv^2 + ma$AnswerVerified575.7k+ viewsHint: In dimensional analysis, mass is represented by M, length by L and Time by T. For example velocity is represented as L/T or $[M^0LT^{-1}]$. The left hand side of the expression should completely match with the right hand side in dimensions.Complete step by step answer:Given, $J= kg m^2 s^{-2}$The dimensions for this expression can be written as $[ML^2T^{-2}]$. As we simply translated the respective units into dimensions like kg became M, m (not mass here) corresponds to L and s is a unit of time so T was placed.We analyze all the options one by one dimensionally;(A) $K=m^2 v^3$m is mass, v is velocity so, the dimensions are $[M^2L^3T^{-3}]$.This clearly does not match with $[ML^2T^{-2}]$. (B) $K= (1/2) mv^2$This is our familiar kinetic energy expression, so it is obviously correct as dimensions are $[ML^2T^{-2}]$.(C) $K=ma$We are aware that ma is used for force. The dimensions will be $[MLT^{-2}]$. So this can be discarded too.(D) $K=(3/16) m v^2$This might not look as familiar as (B) but this is a dimensionally correct kinetic energy expression. Only constant in the front is 3/16 here in place of 1/2. This does not affect dimensional analysis.(E) $K= (1/2) mv^2 + ma$An important point to be noted from this expression is that the dimensions of all the terms on the LHS and RHS should match. The second term in the RHS is ma, which will give dimensions of force i.e., $[MLT^{-2}]$. Therefore making the entire expression dimensionally incorrect.Therefore, the correct answers to be chosen here are (A), (C) and (E) as all these can be ruled out based on dimensional arguments.Note:Read the question carefully. It is specifically asked to choose the wrong expression. One can tick the correct expression instead, when in a hurry. Also the (3/16) factor does not affect the dimensions so that should be kept in mind.Recently Updated PagesMaster Class 12 Business Studies: Engaging Questions & Answers for SuccessMaster Class 12 Economics: Engaging Questions & Answers for SuccessMaster Class 12 English: Engaging Questions & Answers for SuccessMaster Class 12 Maths: Engaging Questions & Answers for SuccessMaster Class 12 Social Science: Engaging Questions & Answers for SuccessMaster Class 12 Chemistry: Engaging Questions & Answers for SuccessMaster Class 12 Business Studies: Engaging Questions & Answers for SuccessMaster Class 12 Economics: Engaging Questions & Answers for SuccessMaster Class 12 English: Engaging Questions & Answers for SuccessMaster Class 12 Maths: Engaging Questions & Answers for SuccessMaster Class 12 Social Science: Engaging Questions & Answers for SuccessMaster Class 12 Chemistry: Engaging Questions & Answers for Success

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