Two objects of masses m1 and m2 move in circles having different radii r1 and r2

Question

  Two objects of masses m1 and m2 move in circles having different radii r1 and r2.m1 is greater than m2 and r1 is greater than r2. Acted on by different centripetal forces F1 and F2, they move at different speeds v1 and v2. However the accelerations a1 and a2 are equal. Is v1 less than, greater than, or equal to v2 (or is it impossible to be sure?). Is F1 less than, greater than or equal to F2 (or is it impossible to be sure?). If the ratio of the radii is r1/r2=4 what must be the ratio of the velocities v1/v2? If the ratio of the masses is m1/m2=4 what must be the ratio of the centripetal forces F1/F2?

Explanation / Answer

Given:m1>m2,r1>r2,a1=a2 a=v2/r a1=a2  =>v12/r1=v22/r2  =>v1/v2=(r1/r2)>1.........(becauser1>r2) So v1>v2 F=mv2/r=ma =>F1/F2=m1a1 /m2a2=m1/m2>1...........(becausea1=a2 and m1>m2) So F1>F2 If r1/r2=4 v1/v2=4=2 If m1/m2=4 F1/F2=m1/m2=4................

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