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InterviewSolution
| 1. |
Derive dimension formula of work and force |
| Answer» The dimensional formula of Work is given by,M1\xa0L-2\xa0T-2Where,\tM = Mass\tL = Length\tT = TimeDerivationWork (W) = Force\xa0× Displacement . . . . . (1)Since, Force = Mass × acceleration = M × [L T-2]∴ The\xa0dimensional formula\xa0of Force = M1\xa0L1\xa0T-2\xa0. . . . (2)On substituting equation (2) in equation (1) we get,Work = Force\xa0× DisplacementOr, W = [M1\xa0L1\xa0T-2] × [M0\xa0L1\xa0T0]\xa0= [M1\xa0L2\xa0T-2].Therefore, work is dimensionally represented as\xa0[M1\xa0L2\xa0T-2].The dimensional formula of force is given by,M1\xa0L1\xa0T-2Where,\tM = Mass\tL = Length\tT = TimeDerivationForce = Mass × Acceleration . . . . (1)Since, acceleration = velocity × [time]–1\xa0= [LT-1] × [T]-1Therefore, the\xa0dimensional formula\xa0of acceleration = [LT-2] . . . . (2)On substituting equation (2) in equation (1) we get,Force = m × aOr, F = [M] × [L1\xa0T-2] = M1\xa0L1\xa0T-2.Therefore, Force is dimensionally represented as\xa0M1\xa0L1\xa0T-2. | |