If an object of mass 10 kg is moving with a uniform speed of 10 m/s, t

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

100 N.s and 500 J
100 N.s and 1000 J
200 N.s and 500 J
200 N.s and 1000 J
This question was previously asked in
UPSC CDS-2 – 2022
We are given the mass and uniform speed of an object and asked to calculate its linear momentum and kinetic energy.
– Linear momentum (p) is given by the product of mass (m) and velocity (v). The unit of linear momentum is kg.m/s, which is equivalent to N.s (Newton-second).
Given m = 10 kg and v = 10 m/s,
p = m * v = 10 kg * 10 m/s = 100 kg.m/s = 100 N.s.

– Kinetic energy (KE) is given by the formula 0.5 * m * v². The unit of kinetic energy is Joules (J).
Given m = 10 kg and v = 10 m/s,
KE = 0.5 * 10 kg * (10 m/s)² = 0.5 * 10 kg * 100 m²/s² = 5 * 100 J = 500 J.

Therefore, the linear momentum is 100 N.s and the kinetic energy is 500 J.

Linear momentum is a vector quantity (direction matters), while kinetic energy is a scalar quantity. The N.s unit for momentum comes from the impulse-momentum theorem, where Impulse (Force x time) equals the change in momentum. 1 Newton = 1 kg.m/s², so 1 N.s = (kg.m/s²) * s = kg.m/s.
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