A) \[{{T}_{h}}=1.5\text{ }{{T}_{c}}\]
B) \[{{T}_{h}}={{T}_{c}}\]
C) \[{{T}_{h}}=2{{T}_{c}}\]
D) \[{{T}_{h}}=0.5{{T}_{c}}\]
Correct Answer: B
Solution :
\[{{M}_{C}}=2M\text{ }\And {{M}_{H}}=M\] Using \[T=2\pi \sqrt{\frac{I}{MB}}\] \[\therefore \,\,\,\,\frac{{{T}_{H}}}{{{T}_{C}}}=\sqrt{\frac{{{I}_{H}}}{{{M}_{H}}}\,\,\frac{{{M}_{C}}}{{{I}_{C}}}}\] \[=\,\,\sqrt{\frac{m{{R}^{2}}}{\frac{1}{2}m{{R}^{2}}\,2M}}\,\,=\,\,\frac{1}{1}\] \[{{T}_{\ell }}=Tc\]
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