Question

In a new system of units, the unit of mass equals α kg, the unit of length equals β m and unit of time equals γ second. The value of 1 newton in this new system of units is

Answer 1

Step-by-step explanation:

Given that,

Given that,1 Calorie=4.2 J = 4.2 Kg m2 s-2                …… (i)

Given that,1 Calorie=4.2 J = 4.2 Kg m2 s-2                …… (i)As new unit of mass = α Kg

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

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 massSimilarly, 1 m = β-1 new unit of length

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 massSimilarly, 1 m = β-1 new unit of length1 s = γ-1 new unit of time

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 massSimilarly, 1 m = β-1 new unit of length1 s = γ-1 new unit of timePutting these values in (i), we get

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 massSimilarly, 1 m = β-1 new unit of length1 s = γ-1 new unit of timePutting these values in (i), we get1 calorie = 4.2 (α-1 new unit of mass) (β-1 new unit of length)2 (γ-1 new unit of time)-2

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 massSimilarly, 1 m = β-1 new unit of length1 s = γ-1 new unit of timePutting these values in (i), we get1 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)