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A Calorie Is A Unit Of Heat Or Energy And It Equals About 4.2 J Where 1j = 1 Kg M2 S–2. Suppose We Employ A System Of Units In Which The Unit Of Mass Equals α Kg, The Unit Of Length Equals β M, The Unit Of Time Is γ S. Show That A Calorie Has A Magnitude 4.2 α–1 β–2 γ2 In Terms Of The New Units? |
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Answer» Considering the unit CONVERSION formula, n1U1 = n1U2 N1[M1aL1bT1c] = n2[M2aL2bT2c] Given here, 1 Cal = 4.2 J = 4.2 KG m2 s–2. n1 = 4.2, M1 = 1kg, L1 = 1m, T1 = 1 sec and n2 = ?, M2 = α kg, L2 = βm, T2 = γ sec The dimensional formula of ENERGY is = [M1L2T-2] ⇒ a = 1, b =1 and c = -2 Putting these values in above equation, n2= n1[M1/M2]a[L1/L2]b[T1/T2]c = n1[M1/M2]1[L1/L2]2[T1/T2]-2 = 4.2[1Kg/α kg]1[1m/βm]2[1sec/γ sec]-2 = 4.2 α–1 β–2 γ2 Considering the unit conversion formula, n1U1 = n1U2 n1[M1aL1bT1c] = n2[M2aL2bT2c] Given here, 1 Cal = 4.2 J = 4.2 kg m2 s–2. n1 = 4.2, M1 = 1kg, L1 = 1m, T1 = 1 sec and n2 = ?, M2 = α kg, L2 = βm, T2 = γ sec The dimensional formula of energy is = [M1L2T-2] ⇒ a = 1, b =1 and c = -2 Putting these values in above equation, n2= n1[M1/M2]a[L1/L2]b[T1/T2]c = n1[M1/M2]1[L1/L2]2[T1/T2]-2 = 4.2[1Kg/α kg]1[1m/βm]2[1sec/γ sec]-2 = 4.2 α–1 β–2 γ2 |
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