Two blocks with masses 100 g and 200 g are attached to the ends of springs A and B as shown in the figure. [2026]

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Solution

Q.
Two blocks with masses 100 g and 200 g are attached to the ends of springs A and B as shown in the figure. The energy stored in A is E. The energy stored in B, when spring constants $k_{A}$ and $k_{B}$ of A and B, respectively satisfy the relation $4 k_{A} = 3 k_{B}$ is: [2026]

1 $2 E$

2 $4 E$

3 $\frac{4}{3} E$

4 $3 E$

Ans.
(4)

$For equilibrium k x = m g$

$U = \frac{1}{2} k x^{2} = \frac{1}{2} \frac{m^{2} g^{2}}{k}$

$U \propto \frac{m^{2}}{k}$

$\frac{U_{A}}{U_{B}} = {(\frac{m_{A}}{m_{B}})}^{2} (\frac{k_{B}}{k_{A}}) = {(\frac{1}{2})}^{2} (\frac{4}{3}) = \frac{1}{3}$

$\frac{E}{U_{B}} = \frac{1}{3} \Rightarrow U_{B} = 3 E$

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