Verify that the cyclotron frequency omeg...

Verify that the cyclotron frequency `omega=eB//m` has the correct dimensions of `[T]^-1`.

Text Solution

Verified by Experts

If a charged particle of mass m and charge q is moving perpendicular to the magnetic field B with a velocity v, then the magnetic force acting on the particle will make it move in a circular path of radius r.
`rArr qvB = (mv^(2))/r " or " (qB)/m = v/r = omega ` (angular frequency)
` :. ` Dimensions of ` omega = (qB)/m = v/r = (LT^(-1))/L = [T^(-1)]`

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E.M.F has dimensions of

`M^(1)L^(2)T^(-3)A^(-1)`

`M^(2)L^(2)T^(-3)A^(-1)`

`M^(2)L^(2)T^(3)A^(-1)`

`M^(2)L^(-2)A^(-1)`

Which one of the following has the dimensions of ML^(–1)T^(–2) ?

torque

surface tension

viscosity

stress

Which one of the following has the dimensions of ML^(-1) T^(-2) ?

Torque

Surface tension