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You have not specified if the wheel is hollow or not.
Anyway, I will do it for both the cases. Now when the force is applied tangentially, it will produce a torque which will produce angular deceleration if the force is in the right direction.
Now, w = 100/60 rps = 5/3 rps. angular displacement - 10 rev.
w1 (final angular velocity) = 0.
So, using w12-w2 = 2qa,
(here q = 10)
we get a = 5/36
We also know that torque = Ia = FR
If the wheel is hollow,I=mr2
putting this , we get F = 5/18 newton.
If wheel is not hollow, I = mr2/2,
which gives F = 5/36N
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