Question

A particle is moving in a radius R with constant speed v. The magnitude of average acceleration after half revolution is ____________.

A particle is moving in a circle of radius 'R' with constant speed 'V'. The magnitude of average speed after half revolution is ______.

विकल्प

• `(2π)/("Rv"^2)`

• `(2"R")/(π"v")`

• `(2"v"^2)/(π"R")`

• `(2"v")/(π"R"^2)`

Answer 1

A particle is moving in a radius R with constant speed v. The magnitude of average acceleration after half revolution is `underline((2"v"^2)/(π"R"))`.

Explanation:

The given situation is shown in the figure.

In a half-revolution, the momentum of a particle changes.

Δp = mv − m(−v) = 2mv .................(i)

The amount of time it takes for a particle to complete a half-revolution,

t = `(π"R")/"v"` .........(ii)

∴ Average force (F) = Rate of change in momentum

= `(Δ"p")/"t"`

= `(2"mv")/(π"R"/"v")` ............[From Eqs. (i) and (ii)]

F = `(2"mv"^2)/(π"R") = "ma" = (2"mv"^2)/(π"R")` .......[F = ma]

a = `(2"v"^2)/(π"R")`