Physics · Work, Energy And Power · NEET
No. Momentum p = mv is a vector (has direction) with unit kg m/s. Kinetic energy KE = (1/2)mv^2 is a scalar (no direction) with unit joule. They are linked by KE = p^2 / (2m), but they are different quantities. This is why momentum can be zero for a system while kinetic energy is not (two equal masses moving opposite ways).
Start from KE = (1/2)mv^2 and p = mv, so v = p/m. Substitute: KE = (1/2)m(p/m)^2 = p^2 / (2m). The v^2 in kinetic energy becomes p^2 after substitution. That squaring is why doubling momentum makes KE four times larger, not two times.
For the same mass, KE = p^2 / (2m), so KE depends on p^2. If p becomes 2p, then KE becomes (2p)^2 / (2m) = 4 times the original KE. So doubling momentum makes kinetic energy 4 times bigger.
Use p = sqrt(2 m KE). With KE fixed, p is proportional to sqrt(m). The heavier body has larger momentum. Example: same KE, one body 4 times heavier has 2 times the momentum. This is a favourite NEET one-liner.
Use KE = p^2 / (2m). With p fixed, KE is inversely proportional to m. The lighter body has greater kinetic energy. So for equal momentum, the smaller mass carries more KE.
Try the real previous-year questions from this chapter — each with the answer and a full solution.
KE = p^2 / (2m) and p = sqrt(2 m KE), where m is mass, p is momentum and KE is kinetic energy.
From p = mv, write v = p/m. Put this in KE = (1/2)mv^2 to get KE = (1/2)m(p/m)^2 = p^2 / (2m).
KE is proportional to p^2. If p becomes 1.10p, KE becomes (1.10)^2 = 1.21 times, a 21 percent increase.
Since KE = p^2 / 2m at fixed p, KE is inversely proportional to mass, so the lighter body has more kinetic energy.
Momentum is a vector (magnitude and direction). Kinetic energy is a scalar. This is a common one-mark distinction in NEET.
