Question
A wire elongates by $$l \,mm$$ when a load $$W$$ is hanged from it. If the wire goes over a pulley and two weights $$W$$ each are hung at the two ends, the elongation of the wire will be (in $$mm$$ )-
A.
$$l$$
B.
$$2l$$
C.
$$zero$$
D.
$$\frac{l}{2}$$
Answer :
$$l$$
Solution :
Case (i) At equilibrium, $$T= W$$
$$Y = \frac{{\frac{W}{A}}}{{\frac{\ell }{L}}}\,.....\,(1)$$
Case (ii) At equilibrium, $$T= W$$
$$Y = \frac{{\frac{W}{A}}}{{\frac{{\frac{\ell }{2}}}{{\frac{L}{2}}}}}\,\,\,\, \Rightarrow Y = \frac{{\frac{W}{A}}}{{\frac{\ell }{L}}}$$
$$ \Rightarrow $$ Elongation is the same.
Case (i) At equilibrium, $$T= W$$
$$Y = \frac{{\frac{W}{A}}}{{\frac{\ell }{L}}}\,.....\,(1)$$
Case (ii) At equilibrium, $$T= W$$
$$Y = \frac{{\frac{W}{A}}}{{\frac{{\frac{\ell }{2}}}{{\frac{L}{2}}}}}\,\,\,\, \Rightarrow Y = \frac{{\frac{W}{A}}}{{\frac{\ell }{L}}}$$
$$ \Rightarrow $$ Elongation is the same.
