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An object of mass m is moving in unifrom...

An object of mass m is moving in unifrom circular motion in xy-plane. The circle has radius R and object is moving clockwise around the circle with speed v. The motion is projected onto the x-axis where it appears as simple harmonic motion accoding to `x(t) = Rcos (omegat + phi)`. The motion starts from pointof coordinates
`(0,R)`
In this projection `omega` is -

A

`v//R`

B

`m^(2)//R`

C

`R//v`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
A
`omega = (2pi)/(T) = (2pi)/((2piR//v)) = v/R`
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Knowledge Check

  • An object of mass m is moving in unifrom circular motion in xy-plane. The circle has radius R and object is moving clockwise around the circle with speed v. The motion is projected onto the x-axis where it appears as simple harmonic motion accoding to x(t) = Rcos (omegat + phi) . The motion starts from pointof coordinates (0,R) . In this projection phi is-

    A
    `pi//2`
    B
    `pi`
    C
    `3pi//2`
    D
    `0`

  • For a particle in uniform circular motion , the acceleration vec(a) at a point p ( R, theta ) on the circle of radiu R is ( Here theta is measured from the x- axis )

    A
    `-(v^(2))/(R ) cos theta hat(i) + (v^(2))/(R ) sin theta hat(j)`
    B
    `-(v^(2))/(R ) sin theta hat(i) + (v^(2))/(R ) cos theta hat(j)`
    C
    `-(v^(2))/(R ) cos theta hat(i) - (v^(2))/(R ) sin theta hat(j)`
    D
    `-(v^(2))/(R ) hat(i) + (v^(2))/(R ) hat(j)`

  • For a particle in uniform circular motion the acceleration vec a at a point P ( R, theta ) on the circle of radius R is : ( here theta is measured from the x- axis )

    A
    ` - (v^ 2 )/(R ) cos theta hati + (v^2 ) /(R ) sin theta hatj `
    B
    ` - ( v ^ 2 ) /( R ) sin theta hati + (v ^ 2 )/( R ) cos theta hatj `
    C
    ` - (v ^ 2 )/( R ) cos theta hai - (v ^ 2 ) / ( R ) sin theta hatj `
    D
    ` (v^ 2 )/ (R ) hati + (v ^ 2 ) /( R ) hatj `

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