Physics Elasticity Question 117
Question: A wire of length L and radius r is rigidly fixed at one end. On stretching the other end of the wire with a force F, the increase in its length is l. If another wire of same material but of length 2L and radius 2r is stretched with a force of 2F, the increase in its length will be
[NCERT 1980; AIIMS 1980; MP PET 1989, 92; MP PET/PMT 1988; MP PMT 1996, 2002; UPSEAT 2002]
Options:
A) l
B) 2l
C) $ \frac{l}{2} $
D) $ \frac{l}{4} $
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Answer:
Correct Answer: A
Solution:
$ l=\frac{FL}{AY}=\frac{FL}{\pi r^{2}Y}\
Therefore l\propto \frac{FL}{r^{2}} $ (Y = constant) $ \frac{l _{2}}{l _{1}}=\frac{F _{2}}{F _{1}}\times \frac{L _{2}}{L _{1}}{{\left( \frac{r _{1}}{r _{2}} \right)}^{2}}=2\times 2\times {{\left( \frac{1}{2} \right)}^{2}}=1 $ \ $ l _{2}=l _{1} $ i.e. increment in its length will be l.
BETA
