1 calorie = 4.2 j
1J = 1 kg m2s–2
put the value we get =>
1 calorie =4.2 kg m2s–2
= 4.2 × (1 kg) × (1 m2) × (1 s–2) …(1)
Given that
Unit of mass equals α kg =>
1 kg mass = 1/α mass
Unit of length equals β m =>
1 m length = 1/ β length
Unit of time is γs =>
1 s time = 1/ γ time
Put the values in equation (1), we get New unit of mass
= α kg=4.2 × (1 kg) × (1 m2) × (1 s–2)
= 4.2 × (1/ α ) × (1/ β ) 2 × (1/ γ) –2
= 4.2 × ( α–1 ) × (β–1 ) 2 × ( γ–1) –2
=4.2 α–1 β–2 γ2