Saved Bookmarks
| 1. |
An Indian rubber card 10 m long is suspended vertically. How much does it stretch under its own weight? Density of rubber = 1.5 x 103 kg m-3 and Young's modulus of rubber = 6 x 106 g f cm-2 |
|
Answer» Here, L = 10 m; ρ = 1.5 x 103 kg-3 Y = 6 x 106 g f cm-2 = 6 x 106 x 980 dyne cm-2 = 5.88 x 108 Nm-2 Let 'a' be the area of cross-section of the Indian rubber cord. Then, F = weight of the rubber cord = L x a x ρ x g The weight of the rubber cord acts at its centre of gravity and hence the weight of the rubber cord will produce extension in the length L/2 of the cord. Now, Y = {F(L/2)}/al l = {F x L}/{2a x Y} = {L x a x ρ x g x L}/{2a x Y} = {L2ρg}/{2Y} = {102 x 1.5 x 103 x 9.8}/{2 x 5.88 x 108} = 1.25 x 10-3 m = 1.25 mm |
|