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COMEDK2013PhysicsMechanical Properties of Solids

If the ratio of diameters, lengths and Young's modulus of steel and copper wires shown in the figure are p, q and s respectively, then the corresponding ratio of increase in their lengths would be

Options

  1. A5 q 7 s p²
  2. B7 q 5 s p²
  3. C2 q 5 s p
  4. D7 q 5 s p

Correct answer

B. 7 q 5 s p²

Step-by-step solution

Young's modulus, Y= F L A L = 4 F L D² L L= 4 F L D² Y The ratio of increase in length of steel and copper is L_ s L_ c = F_ s L_ s D_ s ² Y_ s D_ c ² Y_ c F_ c L_ c = F_ s F_ c L_ s L_ c ( D_ c D_ s )² Y_ c Y_ s Force on steel wire, F_ s =(2 m+5 m) g=7 m g Force on copper wire, F_ c =5 mg array ll & F_ s F_ c = 7 5 Also, & D_ s D_ c =p, L_ s L_ c =q, Y_ s Y_ c =s & L_ s L_ c = 7 5 q 1 p² 1 s = 7 q 5 s p² array

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