Question

if momentum p area a and time t are taken to be fundamental quantities tha the energy has the dimension

Answer 1

☆☆ AS-SALAMU-ALYKUM ☆☆

ENERGY =1÷2mv^2

Momentum=mv

put this in relation 1

ENERGY =mv .v ------------1

Energy =P . v ---------------2

a=v÷t

v =a × t

v=m/s^2. s

put this in relation 2

Energy = P × a × t ----------3

Now dimensions will be

P=mv

P=[kgm/s]

P=[MLT^_1] --------------a

a=m/s^2

a=[LT^_2]------------b

put a and b in relation 3

Energy =[MLT^_1 LT^_2.T ] -------------4

L^1+1=L^2------------c
T^_1_2.T
T^_3.T
T^_3+1
T^_2 ------------d

put c and d in relation 4


ENERGY =[ML^2T^_2]

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