Check that the ratio ke2 /Gme mp is dimensionless. Determine the value of this ratio. What does the ratio signify?

March 24, 2026Physics

ScanSolve AI Answer

March 24, 2026

Answer

k \frac{q_1 q_2}{r^2} $, so$ k = \frac{F r^2}{q_1 q_2}$.

Step 1: Check that the ratio $\frac{ke^2}{Gm_e m_p}$ is dimensionless.

First, determine the dimensions of each constant and quantity: • Dimensions of Coulomb's constant $k$ : From Coulomb's Law, $F = k \frac{q_1 q_2}{r^2}$ , so $k = \frac{F r^2}{q_1 q_2}$ . $$ [k] = \frac{[MLT^{-2}][L^2]}{[AT][AT]} = \frac{[ML^3 T^{-2}]}{[A^2 T^2]} = [\text{

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Check that the ratio (ke^2)/(Gm_e m_p) is dimensionless. First, determine the dimensions of each constant and quantity: • Dimensions of Coulomb's constant k: From Coulomb's Law, F = k (q_1 q_2)/(r^2), so k = (F r^2)/(q_1 q_2).

Asked on March 24, 2026Physics

This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.

ScanSolve AI AnswerAnswered on March 24, 2026

Step 1: Check that the ratio (ke^2)/(Gm_e m_p) is dimensionless. First, determine the dimensions of each constant and quantity: • Dimensions of Coulomb's constant k: From Coulomb's Law, F = k (q_1 q_2)/(r^2), so k = (F r^2)/(q_1 q_2). [k] = [MLT^-2][L^2][AT][AT] = [ML^3 T^-2][A^2 T^2] = [