A) the mass of the bob should be doubled
B) the length of the pendulum should be doubled
C) the length of the pendulum should be increased by a factor of 4
D) the length of the pendulum should be decreased a factor of 4
E) both the mass and the length of the pendulum should be doubled
Correct Answer: C
Solution :
\[T=2\pi \sqrt{\frac{l}{g}}\] Given, \[{{T}_{1}}=1s,{{l}_{1}}=l,{{T}_{2}}=2s\] \[\therefore \] \[\frac{{{T}_{1}}}{{{T}_{2}}}=\sqrt{\frac{{{l}_{1}}}{{{l}_{2}}}}\] \[\Rightarrow \] \[\frac{1}{2}=\sqrt{\frac{{{l}_{1}}}{{{l}_{2}}}}\] \[\Rightarrow \] \[{{l}_{2}}=4{{l}_{1}}\] Hence, length of pendulum should be increased by a factor of 4.
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