the potential energy of body is given u=x+y^2+z^2, find the force in vector form
Answers
Answer:
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}}⟶[E]=ML2T−2
Hence 1 joule equals,
\longrightarrow\sf{1\ J=1\ kg\,m^2\,s^{-2}}⟶1 J=1 kgm2s−2
In the new system of units,
Unit of mass \sf{=a\ kg.}=a kg.
Unit of length \sf{=b\ m.}=b m.
Unit of time \sf{=c\ s.}=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}}⟶J=(a kg)×(b m)2×(c s)−2
\longrightarrow\sf{J=ab^2c^{-2}\ kg\,m^2\,s^{-2}}⟶J=ab2c−2 kgm2s−2
We know that 1 calorie equals,
\longrightarrow\sf{1\ cal=4.2\ J}⟶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}}}}⟶1 cal=4.2ab2c−2 kgm2s−2