Which of the following pairs of physical quantities does not have same dimensional formula? [NCERT Exemplar]
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a
Work and torque
b
Angular momentum and Planck's constant
c
Tension and surface tension
d
Impulse and linear momentum
answer is A.
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Detailed Solution
(1) Work = Force x Distance = [MLT-2][L] = [ML 2T-2] Torque = Force x Distance = [ML2T-2)(2) Angular momentum = mvr = [M][LT-1][L] = [ML2T-1] Planck's constant =Ev=ML2 T-2T-1=ML2 T-1∣(3) Tension = Force = [ML r2] Surface tension = Force Length =MLT-2[L]=ML0 T-2(4) Impulse = Force x Time = [MLT-2][T] = [MLT-1] Momentum = Mass x Velocity = [M][LT-1] = [MLT-1]Note One should not be confused with the similar form tension in both the physical quantities-surface tension and tension. Dimensional formula for both of them is not same.