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Question

A small body of mass m=0.10 kg moves in the reference frame rotating about a stationary axis with constant angular velocity ω=5.0 rad/s. What work does the centrifugal force of inertia perform during the transfer of this body along an arbitrary path from point 1 to point 2 which are located at the distance r1=30 cm and r2=50 cm from the axis of rotation?

A
0.15 J
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B
0.4 J
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C
0.2 J
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D
0.35 J
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Solution

The correct option is C 0.2 J
Given mass, m=0.1 kg
Angular velocity, ω=5 rad/s
Considering the rotating frame of reference X-Y rotating about the origin O.

Let the body covers arbitrary path AB as shown above while moving in he rotating frame of reference where r1 and r2 represents the position vector of starting and end point.
Considering a small element ds of the path AB. Let the element ds makes an angle θ with the centrifugal force vector directed along the radial direction as shown below.
Work done by centrifugal force to move the body by displaccement ds will be, dW=F.ds
dW=Fdscosθ(1)
Centrifugal force, F=mω2r
dW=mω2rdscosθ(2)
Now radial vector component for the displacement ds will be,
dr=dscosθ
Therefore equation (2) becomes,
dW=mω2rdr
Integrating the above equation from r1 to r2,
dW=r2r1mω2rdr
W=mω2[r22]0.50.3
W=0.1×52×[0.250.092]
W=0.2 J

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