A) 16/81
B) 8/27
C) 19/27
D) 243/256
Correct Answer: D
Solution :
\[{{G}_{1}}={{G}_{2}},\] \[{{l}_{1}}={{l}_{2}},\] \[{{D}_{1}}={{D}_{2}},\] \[{{d}_{1}}=\frac{1}{3}{{D}_{1}}\] \[{{d}_{2}}=\frac{1}{2}{{D}_{2}},\] \[{{T}_{1}}={{T}_{2}}=T\] \[\frac{T}{J}=\frac{G,}{l}\] G, l and T being same for born the shafts, \[\theta =\,\,\propto \frac{1}{J}\] \[\frac{{{\theta }_{1}}}{{{\theta }_{2}}}=\frac{{{J}_{2}}}{{{J}_{1}}}=\frac{\frac{\pi }{32}D_{2}^{4}\,\left[ 1-{{\left( \frac{{{d}_{2}}}{{{D}_{2}}} \right)}^{4}} \right]}{\frac{\pi }{32}D_{1}^{4}\,\left[ 1-{{\left( \frac{{{d}_{1}}}{{{D}_{1}}} \right)}^{4}} \right]}\] \[\frac{\left[ 1-{{\left( \frac{1}{2} \right)}^{4}} \right]}{\left[ 1-{{\left( \frac{1}{3} \right)}^{4}} \right]}=\frac{\left( \frac{15}{16} \right)}{\left( \frac{80}{81} \right)}=\frac{243}{256}\]You need to login to perform this action.
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