Two bodies A,B of masses m1 and m2 are knotted to a mass less string at different points rotated along concentric circles in horizontal plane .The distances of A,B from common centre are 50cm ,1m. If the tensions in string between centre to A and A to B are in ratio 5:4,then the ratio of m1 to m2 is
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The ratio of m1 to m2 is 1/2.
Explanation:
The tension will be more between center to A as it has to bear the centripetal force of 2 bodies.
Applying force balance on the masses.
T1 − T2 = m 1 ω^ 2 r 1
T 2 = m2 ω^2 r2 .........(1)
T2 / T1 = 4/5
Now r1 = 0.5
r2 = 1
=> 5 / 4 = m1(0.5) / m2 + 1
m1 / m2 = 2 x 1 / 4 = 2/4 = 1/2
Hence the ratio of m1 to m2 is 1/2.
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