# A spring having a spring constant 'k' is loaded with a mass 'm'. The spring is cut into two equal parts and one of these is loaded again with the same mass. The new spring constant is Option 1) $\frac{k}{}2$ Option 2) $k$ Option 3) $2k$ Option 4) $k^{2}$

$Spring\;Constant (k)\; \alpha\;\frac{1}{length\; of\; the\; spring\;(l)}$

as length becomes half, $k$ becomes twice i.e $2k$

Time period of oscillation for spring mass system -

$T= 2\pi \sqrt{\frac{m}{K}}$

- wherein

m = mass of block

K = spring constant

Option 1)

$\frac{k}{}2$

This is incorrect.

Option 2)

$k$

This is incorrect.

Option 3)

$2k$

This is correct.

Option 4)

$k^{2}$

This is incorrect.

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