A physical quantity of the dimensions of length that can be formed out of c, G and \(\frac{e^2}{4 \pi \epsilon_o}\) [c is velocity of light, G is universal constant of gravitation and e is charge]
Answer & explanation
Correct answer: option 2
G = M-1 L3 T-2
c = L1 T-1
\(\frac{e^2}{4πε_o}\) = M1 L3 T-2
l ∝ cP GQ [\(\frac{e^2}{4πε_o}\)]R
l ∝ LP T-P (M-1 L3 T-2)Q (M1 L3 T-2)R
M0 L1 T0 = M-Q+R LP+3Q+3R T-P-2Q-2R
-Q + R = 0
Q = R
P+3Q+3R = 1
-P-2Q-2R = 0
On solving, Q = R = \(\frac{1}{2}\), P = -2
l ∝ \(\frac{1}{c^2}\) [G \(\frac{e^2}{4 \pi \epsilon_o}\)]1/2