JEE MAIN - Physics (2006 - No. 24)
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 $$mm$$)
$$l$$
$$2l$$
zero
$$l/2$$
Explanation
Case $$(i)$$
At equilibrium, $$T=W$$
$$Y = {{W/A} \over {\ell /L}}{\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} {\mkern 1mu} ...\left( 1 \right)$$
Case $$(ii)$$ At equilibrium $$T=W$$
$$\therefore$$ $$Y = {{W/A} \over {{{\ell /2} \over {L/2}}}} \Rightarrow Y = {{W/A} \over {\ell /L}}$$
$$ \Rightarrow $$ Elongation is the same.
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