A) \[\frac{100}{3}\] cm
B) \[\frac{200}{3}\]cm
C) 50 cm
D) 75 cm
Correct Answer: B
Solution :
Given that, length of rod AB = 100 cm Taking moment about point O with \[{{T}_{1}}\]and \[{{T}_{2}}\]tension in steel and brass wires respectively. \[{{T}_{1}}(x)={{T}_{2}}(100-x)\] \[\frac{{{T}_{1}}}{{{T}_{2}}}=\frac{100-x}{x}\] ?(i) For equal stress in both the wires, \[\frac{{{T}_{1}}}{{{A}_{1}}}=\frac{{{T}_{2}}}{{{A}_{2}}}\] where \[{{A}_{1}}\]and \[{{A}_{2}}\]are cross-sectional areas of steel and brass wires respectively. or \[\frac{{{T}_{1}}}{{{T}_{2}}}=\frac{{{A}_{1}}}{{{A}_{2}}}\] \[\therefore \] \[\frac{{{T}_{1}}}{{{T}_{2}}}=\frac{0.1}{0.2}=\frac{1}{2}\] ?(ii) From Eq. (ii), substituting the value of\[\frac{{{T}_{1}}}{{{T}_{2}}}\] in Eq. (i). \[\therefore \] \[\frac{1}{2}=\frac{100-x}{x}\] or \[x=200-2x\] or \[x=\frac{200}{3}\,cm\]You need to login to perform this action.
You will be redirected in
3 sec