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in Laws of motion by (15.2k points)
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A person applies a constant force \(\vec F\) on a particle of mass m and finds that the particle move in a circle of radius r with a uniform speed v. 

(A) This is not possible 

(B) There are other forces also on the particle 

(C) The resultant of other forces is mv2/r towards center 

(D) The resultant of the other forces varies in magnitude as well as direction

2 Answers

+1 vote
by (39.0k points)
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Best answer

Correct options are (B) and (D)

Consider the figure, with force F on the particle at different instants of time.

So it is evident that there should be some other forces such that particle will have uniform circular motion

\(\therefore \vec F + \vec F_2= m\vec a\)

Since it’s a uniform circular motion

Now resultant of both the forces \(\vec F\) and \(\vec F_2\) is \(\frac{mv^2}{r}\) which in turn keeps changing both in direction as well as magnitude.

∴ \(\vec F_2=\frac{mv^2}{r}\hat e_r - \vec F\)

Angle between \(\hat e_r\) and \(\vec F\) keeps varying.

+1 vote
by (15.7k points)

Correct option is

(B) There are other forces also on the particle 

(D) The resultant of the other forces varies in magnitude as well as direction

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