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A toy cart is tied to the end of an unstretched string of length ' \( l \) ', when revolved, the toy cart moves in horizontal circle with radius ' \( 2 l \) ' and time period \( T \). If it is speeded until it moves in horizontal circle of radius ' \( 3 l \) ' with period \( T_{1} \), relation between \( T \) and \( T_{1} \) is (Hooke's law is obeyed)
[MHCET 2015]
(a) \( T_{1}=\frac{2}{\sqrt{3}} \)
(b) \( T_{1}=\sqrt{\frac{3}{2}} T \)
(c) \( T_{1}=\sqrt{\frac{2}{3}} T \)
(d) \( T_{1}=\frac{\sqrt{3}}{2} T \)
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