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A metal ball of mass 2kg moving with speed of36km/hr is having a collision with a stationaryball of mass 3kg. If after collision, both the ballsmove together, the loss in kinetic energy due tocollision is:DolBlim 25 401 916 4) 1601 |
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Answer» Let us suppose the following things,Mass of smaller ball, m₁ = 2kgMass of larger ball, m₂ = 3kgCombined mass of two balls, m₃ = 5kg Initial Velocity of Smaller Ball, u₁ = 36 km/h = 10m/sInitial Velocity of Larger Ball, u₂ = 0 m/sFinal Velocity of both balls combined, v = (?) By, Law of Conservation Of Momentum, (For this case) m₁u₁ + m₂u₂ = m₃v∴2 * 10 + 3 * 0 = 5 * v∴20 + 0 = 5v∴5v = 20∴v = 4 m/s Thus, the final velocity of both the balls moving as a single mass should be 4 m/s. Now, let us suppose the following, Initial combined velocity, v₁ = 10 m/s (Larger ball was at rest)Final combined velocity, v₂ = 4m/sCombined Mass, m 5kgInitial Kinetic Energy, K₁Final Kinetic Energy, K₂ Change in Kinetic Energy,ΔK = K₂ - K₁ = 1/2 mv₂² - 1/2 mv₁² = 1/2 m (v₂² - v₁²) = 1/2 * 5 (4² - 10²) = 5/2 * (16 - 100) = 5/2 * (-84) = 5 * (-42) ∴ΔK = -210 J Thus change in Kinetic Energy is 210 J. |
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