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The linear velocity of a rotating body i...

The linear velocity of a rotating body is given by `vec(v)= vec(omega)xxvec(r )`, where `vec(omega)` is the angular velocity and `vec(r )` is the radius vector. The angular velocity of a body is `vec(omega)= hat(i)-2hat(j)+2hat(k)` and the radius vector `vec(r )= 4hat(j)-3hat(k)`, then `|vec(v)|` is

A

`sqrt(29)` units

B

`sqrt(31)` units

C

`sqrt(37)` units

D

`sqrt(41)` units

Text Solution

Verified by Experts

The correct Answer is:
A
`vecv=vecomegaxxvecr={:|(hati,hatj,hatk),(1,-2,3),(0,4,-3):}|`
`=hati(6-8)-hatj(-3)+4hatk-2hati+3hatj+4hatk`
`|vecV|=sqrt((-2)^(2)+(3)^(2)+4^(2))=sqrt(29)` units
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