Question

prove that 1N=10 to the power 7 erg

Answer 1

We have to prove that
1 Joule = 10 to the power 7 erg
PROOF:
Let's suppose that 1 Joule = X erg -------------------------(1)
Since,
[E] = M L² T to the power -2
Putting this value in equation (1), we get :
(1) (M1 L1² T1 to the power-2) = (X) (M2² L2² T2 to the power-2)
X = (M√M²) (L1²/L2²) (T1 to the power -2/T2 to the power -2)
= (kg/gm) (m/cm)² (s/s) to the power -2
= (1000gm/1gm) (100cm/1cm)² (1) to the power -2
= (10)³ (10²)² (1)
= (10)³ (10)⁴
= (10) to the power 3+4
= (10) to the power 7

Hence proved.