A physical quantity having dimensions of length is to be formed from c, G and e²/(4πε₀), where c is speed of light, G is gravitational constant and e is charge. Which expression has dimensions of length?
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Question

A physical quantity having dimensions of length is to be formed from c, G and e²/(4πε₀), where c is speed of light, G is gravitational constant and e is charge. Which expression has dimensions of length?

Options

G1 Physics · Accepted Answer

Step 1: [e²/(4πε₀)] has dimensions of force×distance² = [M L³T⁻²]. Step 2: Multiplying by G gives [L⁶T⁻⁴]; square root gives [L³T⁻²]. Step 3: Dividing by c²=[L²T⁻²] leaves [L]. Final: Thus option A.