Find the ratio of the extension in upper spring to lower spring.

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Solution

Q.
Find the ratio of the extension in upper spring to lower spring.

1 $\frac{m_{1} k_{1}}{m_{2} k_{2}}$

2 $\frac{m_{2} k_{1}}{m_{1} k_{2}}$

3 $\frac{(m_{1} + m_{2}) k_{2}}{m_{1} k_{1}}$

4 $\frac{(m_{1} + m_{2}) k_{2}}{m_{2} k_{1}}$

Ans.
(4)

$k_{1} x_{1} = k_{2} x_{2} + m_{1} g; k_{2} x_{2} = m_{2} g$

$x_{1} = \frac{k_{2}}{k_{1}} [\frac{m_{2} g}{k_{2}}] + \frac{m_{1} g}{k_{1}}$

$x_{2} = \frac{m_{2} g}{k_{2}}$

$x_{1} = \frac{(m_{1} + m_{2}) g}{k_{1}}$

$\frac{x_{1}}{x_{2}} = \frac{(m_{1} + m_{2}) k_{2}}{k_{1} m_{2}}$

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