If the unit of Force, Energy and Velocity is 20 N . . .

Question : If the unit of Force, Energy and Velocity is 20 N, 200 J and 5 m/s. Find the unit of length, mass and time. 

Doubt by Kartik

Solution : 

Force = 20 N

[MLT^-2] = 20 — (1)

Energy = 200 J

[ML²T^-2] = 200 — (2)

Velocity = 5 m/s
[LT^-1] = 5 — (3) 

Squaring both sides

[L²T^-2] = 25 — (4)

Dividing equation (2) by (4)
[M] = 8 kg

Dividing equation (2) by (1)

[L] = 200/20
[L] = 10 m

Putting L=10 in equation (3)

[LT^-1]=5
[L][T^-1]=5
10[T^-1]=5
10/5=1/[T^-1]
2 = [T]
[T] = 2 s

Hence, [M] = 8 kg, [L] = 10 m, [T] = 2 s