Question

If v, P and K denote velocity, momentum and
kinetic energy of a particle, then
(1) p = dK/dt
(2) P.dv = dk
(3) p = dv/dt
(4) None of these​

Answer 1

answer : option (2) Pdv = dK

it is given that,

v is velocity , P is momentum and K is kinetic energy of a particle.

we know, kinetic energy = 1/2 × mass of particle ×( speed of particle)²

⇒K = 1/2 mv²

now differentiating both sides ,

⇒dK = d(1/2 mv²)

⇒dK = 1/2 [dm × v² + 2v m dv]

⇒dK = 1/2 × 2mv dv [ mass is constant so, dm = 0 ]

⇒dK = mv dv .........(1)

now from definition of linear momentum, it is the product of mass and velocity of particle.

so, P = mv ......(2)

putting equation (2) in equation (1) we get,

dK = P dv

hence, option (2) is correct choice.

also read similar questions:What term is used to denote the change of velocity with time

https://brainly.in/question/1181843

Define kinetic energy. Write an expression for kinetic energy and the S.I. unit of kinetic energy ,

https://brainly.in/question/11384416

Answer 2

$\huge\bold\purple{Answer:-}$

(2) P.dv = dk