A mass is suspended separately by two different springs in successive order, then time period is T1 and T2 respectively.If it is connected by both springs as shown in Fig. then time period is T0. The correct relation is

A
$T_{0}^{2} = T_{1}^{2} + T_{2}^{2}$
B
$T_{0}^{- 2} = T_{1}^{- 2} + T_{2}^{- 2}$
C
$T_{0}^{- 1} = T_{1}^{- 1} + T_{2}^{- 1}$
D
$T_{0} = T_{1} + T_{2}$

Solution:

$T = 2 π \sqrt{\frac{m}{k}} \Rightarrow k \propto \frac{1}{T^{2}}$
In parallel combination, $k = k_{1} + k_{2} \frac{1}{T_{0}^{2}} = \frac{1}{T_{1}^{2}} + \frac{1}{T_{2}^{2}}$

A mass is suspended separately by two different springs in successive order, then time period is T₁ and T₂ respectively.If it is connected by both springs as shown in Fig. then time period is T₀. The correct relation is

Solution:

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