| If the ratio of lengths, radii and Young module of steel and brass wires in the figure are a, b and c respectively, then the corresponding ration of increase in lengths is: |
| [JEE ONLINE 09-04-2013] |
 |
A) \[\frac{3c}{2a{{b}^{2}}}\]
B) \[\frac{2{{a}^{2}}c}{b}\]
C) \[\frac{3a}{2{{b}^{2}}c}\]
D) \[\frac{2ac}{{{b}^{2}}}\]
Correct Answer: C
Solution :
| [c] For steel wire |
| As change in length \[(\Delta {{l}_{1}})=\frac{3Mg{{l}_{1}}}{r_{1}^{2}\pi {{y}_{1}}}\] ...(i) |
| and for beam wire, |
| Change in length \[(\Delta {{l}_{2}})=\frac{2Mg\,{{l}_{2}}}{\pi r_{2}^{2}{{y}_{2}}}\] ...(ii) |
| Dividing Eq. (i) by (ii), we get, r |
| Corresponding ratio of increase in their lengths \[=\frac{3a}{2{{b}^{2}}c}\] |
You need to login to perform this action.
You will be redirected in
3 sec
