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Q.

A block of mass ‘m’ is attached to two unstretched springs of spring constants $k_{1} & k_{2}$ as shown in figure. The block is displaced towards right through a distance x and is released. Find the speed of the block as it passes through the mean position

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a

x \sqrt{\frac{k_{1} + k_{2}}{m}}

b

x \sqrt{\frac{k_{1} - k_{2}}{m}}

c

x \sqrt{\frac{m}{(k_{1} - k_{2})}}

d

x \sqrt{\frac{m}{(k_{1} + k_{2})}}

answer is A.

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Detailed Solution

W = \frac{1}{2} {mv}^{2} = \frac{1}{2} K_{eff} x^{2}

${mv}^{2} = (K_{1} + K_{2}) x^{2}$

$v^{2} = \frac{(K_{1} + K_{2}) x^{2}}{m}$

$v = x \sqrt{\frac{K_{1} + K_{2}}{m}}$

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