Manipal MET2010PhysicsMechanical Properties of Solids
Two wires of lengths l and 2 l , radii r and 2 r respectively having same Young's modulus are hung with a weight m g . Net elongation is
Options
- A3 m g l r^2 Y
- B2 m g l 3 r^2 Y
- C3 m g l 2 r^2 Y
- D3 m g l 4 r^2 Y
Correct answer
C. 3 m g l 2 r^2 Y
Step-by-step solution
Young's modulus, Y= m g l a₁ l₁ l₁= m g l Y r^2 ...(i) and Y= m g(2 l) a₂ l₂ = m g(2 l) (2 r)^2 l₂ or l₂= m g l 2 Y r^2 ...(ii) From Eqs. (i) and (ii), we have l₁+l₂= m g l Y r^2 + m g l 2 Y r^2 = 3 2 m g l Y r^2