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Questions
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 ______.
Options
`(2π)/("Rv"^2)`
`(2"R")/(π"v")`
`(2"v"^2)/(π"R")`
`(2"v")/(π"R"^2)`
Solution
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")`
