Question

If the unit of mass is 'a' kg. the unit of length is 'b' metre and the unit of time is 'c' second, the
magnitude of calorie in new system is (1 Cal = 4.25)
a) 4.2a b c new units
b) 4.2a'b'new units
d)
abc new units
c) abc new units
4.2​

Answer 1

Calorie is a unit of energy, right? We know the SI unit of energy is Joule.

The dimension of energy is,

$\longrightarrow\sf{[\,E\,]=M\,L^2\,T^{-2}}$

Hence 1 joule equals,

$\longrightarrow\sf{1\ J=1\ kg\,m^2\,s^{-2}}$

In the new system of units,

• Unit of mass $\sf{=a\ kg.}$

• Unit of length $\sf{=b\ m.}$

• Unit of time $\sf{=c\ s.}$

Hence unit of energy (magnitude of Joule) in new system is,

$\longrightarrow\sf{J=(a\ kg)\times(b\ m)^2\times(c\ s)^{-2}}$

$\longrightarrow\sf{J=ab^2c^{-2}\ kg\,m^2\,s^{-2}}$

We know that 1 calorie equals,

$\longrightarrow\sf{1\ cal=4.2\ J}$

Hence magnitude of calorie in new system is,

$\longrightarrow\sf{\underline{\underline{1\ cal=4.2\,ab^2c^{-2}\ kg\,m^2\,s^{-2}}}}$