Two bodes with kinetic energies in the ratio of 4: 1 are moving with equal linear momentum. The ration of their masses is:
Correct answer: D. 1 : 4
- A. 1 : 2
- B. 1 : 1
- C. 4 : 1
- D. 1 : 4
Explanation
Given:Kinetic energy ratio: KE_1 / KE_2 = 4/1Linear momentum: p_1 = p_2Relationship between kinetic energy (KE), momentum (p), and mass (m):KE = p^2 / (2m)From this, we can express mass as:m = p^2 / (2KE)Ratio of masses:m_1 / m_2 = (p_1^2 / 2KE_1) / (p_2^2 / 2KE_2)m_1 / m_2 = (p_1^2 / p_2^2) * (KE_2 / KE_1)Since p_1 = p_2, the momentum ratio (p_1/p_2)^2 = 1.The kinetic energy ratio is given as KE_1/KE_2 = 4/1, so KE_2/KE_1 = 1/4.Substituting these values:m_1 / m_2 = (1) * (1/4)m_1 / m_2 = 1/4The ratio of their masses is 1:4.
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About Linear Momentum
Linear momentum is the vector product of mass and velocity, p = mv, and changes when a net external force acts. Work includes impulse as the change in momentum, conservation of momentum in isolated systems, collisions and explosions, and the distinction between elastic, inelastic and perfectly inelastic collisions.
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