1 calorie = 4.2 J where 1J = 1 kg m² s⁻². Suppose we employ a system of units in which the unit of mass is a kg, the unit of length is b m and the unit of time is c s. Show that a calorie has a magnitude 4.2 a⁻¹b⁻²c² in the new system.
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Hii dear,
# Proof-
Presently,
1 cal = 4.2 J = 4.2 kg.m^2/s^2 ...(1)
Suppose in new system fundamental units be Kg', m' and s' for mass, length and time respectively.
Kg' = a Kg Hence, Kg = Kg'/a
m' = b m Hence, m = m'/b
s' = c s Hence, s = s'/c
Putting these values in eqn (1)
1 cal = 4.2 (Kg'/a).(m'/b)^2.(s'/c)^-2
1 cal = 4.2 a^-1.b^-2.c^2 Kg'.m'^2.s'^-2
Hope this is helpful...
# Proof-
Presently,
1 cal = 4.2 J = 4.2 kg.m^2/s^2 ...(1)
Suppose in new system fundamental units be Kg', m' and s' for mass, length and time respectively.
Kg' = a Kg Hence, Kg = Kg'/a
m' = b m Hence, m = m'/b
s' = c s Hence, s = s'/c
Putting these values in eqn (1)
1 cal = 4.2 (Kg'/a).(m'/b)^2.(s'/c)^-2
1 cal = 4.2 a^-1.b^-2.c^2 Kg'.m'^2.s'^-2
Hope this is helpful...
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