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).
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