Q.
Two pulleys of negligible mass are connected to two blocks of mass m1 and m2 by two strings of the same material and the same cross-sectional area as shown in Fig. The speed of a transverse wave in string AB is v1 and that in string CD is v2. The ratio v1v2is
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a
1
b
2
c
2
d
12
answer is D.
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Detailed Solution
Speed of transverse wave in a stretched string is v=Tμ where T is the tension in the string and μ is the mass per unit length of the string. Since strings AB and CD have the same density and the same cross-sectional area, they have the same μ. Hence v∝TIf the tension in CD is T, the tension in string AB is T2.∴ v1v2=TABTCD=T/2T=12So the correct choice is (d).
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