Question

A block of mass $m$ is attached to two unstretched springs of spring constants $k_1$ and $k_2$ as shown in figure.The block is displaced towards right through a distance $x$ and is released. The speed of the block as it passes through the mean position is

• A. $x\sqrt{\frac{k_1}{m}}$
• B. $x\sqrt{\frac{k_2}{m}}$
• C. $x\sqrt{\frac{k_1+k_2}{m}}$
• D. $x\sqrt{\frac{k_1-k_2}{m}}$

Answer 1

Answer: (C)

$U_i=\frac{1}{2}{k}_1{x}^2+\frac{1}{2}{k}_2{x}^2$
$U_f=0;K_i=0;K_f=\frac{1}{2}m{v}^2$
Here, $\Delta U+\Delta K=0$
$\left[0-\left(\frac{1}{2}\left(k_1+k_2\right)x^2\right)\right]+\left[\frac{1}{2}m{v}^2-0\right]=0$
$\Rightarrow \frac{1}{2}m{v}^2=\frac{1}{2}\left(k_1+k_2\right)x^2$
$\Rightarrow v=x\sqrt{\frac{\left(k_1+k_2\right)}{m}}$