A calorie is a unit of heat or energy and it equals about 4.2 J where 1J = 1 kg m2s–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. | Learn NCERT solution | Education portal Class 11 Physics | Study online Unit-2 Units and Measurements



Q.3:- A calorie is a unit of heat or energy and it equals about 4.2 J where 1J = 1 kg m2s–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.

 

Answer:-



Given that,
1 Calorie=4.2 J = 4.2 Kg m2 s-2                …… (i)
As new unit of mass = α Kg
∴ 1 Kg = 1/α new unit of mass
Similarly, 1 m = β-1 new unit of length
1 s = γ-1 new unit of time
Putting these values in (i), we get
1 calorie = 4.2 (α-1 new unit of mass) (β-1 new unit of length)2 (γ-1 new unit of time)-2
= 4.2 α-1 β-2 γ2 new unit of energy (Proved)