Question : A wire of length 2L and radius r, made of material of Young's modulus Y is streched and held straight horizontally without tension between points A and B. A body of mass M, suspended from the middle of the wire depresses the wire to shape ACB as shown in the figure. For the following figure, assume d<<L
(i) The increase in the length of the wire is :
a) d/L
b) d/2L
c) d²/2L
d) d²/L
(ii) The strain in the wire is :
a) d/L
b) d/2L
c) d²/2L²
d) d²/L²
(iii) The tension T in the wire is :
a)MgL/d
b) MgL/2d
c) 2MgL/d
d) MgL/4d
(iv) The stress developed in the wire is :
a) MgL/πr²d
b) MgL/2πr²d
c) 2MgL/πr²d
d) MgL/4π²d
(v) The depression d at the midpoint of the wire is :
a) L[Mg/(πr²Y)]1/3
b) [LMg/(πr²Y)]1/3
c) [Mg/(πr²YL)]1/3
d) 2L[Mg/(πr²Y)]1/3
Doubt by Muskan
Solution :
i) d
ii) c
iii) b
iv) b
v) a
Solution :