Two masses of 1 g and 9 g are moving with equal kinetic energy. The ratio of magnitude of their momentum is

Step-by-step solution

The kinetic energy K of a body of mass m and momentum p is given by the relation K = p^2 2m . Given that the two masses m₁ = 1 g and m₂ = 9 g have equal kinetic energies K₁ = K₂ , we have: p₁^2 2m₁ = p₂^2 2m₂ Rearranging the terms to find the ratio of the magnitudes of their momenta p₁ p₂ : p₁^2 p₂^2 = m₁ m₂ Substituting the given values m₁ = 1 and m₂ = 9 : p₁^2 p₂^2 = 1 9 Taking the square root on both sides: p₁ p₂ = 1 9 = 1 3 Thus, the ratio of the magnitude of their momentum is 1:3 . Answer: 1: 3