Units and Measurement

Question : 3

Total: 33

calorie is a unit of heat or energy and it equals about 4.2 J where 1 J = 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–1β–2γ2 in terms of the new units.

Solution:

We know that n1u1=n2u2
or ‌‌n2=n1

=n1

[M1aL1bT1c ]

[M2aL2bT2c]

=n1[

]a[

]b[

]c
1 cal =4.2 J=4.2kgm2 s−2
∴a=1,b=2,c=−2

SI system	New system
n1=4.2	n2=?
M1=1 kg	M2=α kg
L1=1 m	L2=β m
T1=1 s	L2=γ s

∴‌n2=4.2[

1 kg

α kg

]1 [

1 m

β m

]2 [

1 s

γs

]−2
∴‌n2=4.2α−1 β−2γ2
∴ 1 cal =4.2α−1β−2γ2 in new system
Hence proved.

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