If an object of mass 10 kg is moving with a uniform speed of 10 m/s, then the linear momentum and the kinetic energy of the object, respectively, are
- A.100 N.s and 500 J
- B.100 N.s and 1000 J
- C.200 N.s and 500 J
- D.200 N.s and 1000 J
Correct answer
Explanation
The correct answer is A, 100 N.s and 500 J. Momentum is mass times velocity, 10 × 10 = 100 N.s, and kinetic energy is half the mass times the square of the speed, ½ × 10 × 10 × 10 = 500 J.
Linear momentum, p = mv, measures the quantity of motion and is a vector; its unit kg m/s is the same as the newton-second (N.s), because force multiplied by time gives the change in momentum. Kinetic energy, KE = ½mv², is a scalar measured in joules. The two are linked by KE = p²/2m, and here 100² ÷ (2 × 10) also gives 500 J, which is a quick check.
Option B is wrong because 1000 J forgets the factor of one half. Option C is wrong because 200 N.s doubles the momentum. Option D is wrong because both values are doubled.
Exam tip: p = mv, KE = ½mv² and KE = p²/2m; doubling the speed doubles momentum but makes kinetic energy four times.
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