A spring elongated by length l when a mass ‘M’ is suspended to it. Now a small mass ‘m’ is attached and then released, its time period of oscillation is:

A spring elongated by length l when a mass 'M' is suspended to it. Now a small mass 'm' is attached and then released, its time period of oscillation is:

A
$2 π \sqrt{\frac{(M + m) l}{Mg}}$
B
$2 π \sqrt{\frac{ml}{Mg}}$
C
$2 π \sqrt{\frac{l}{g}}$
D
$2 π \sqrt{\frac{Ml}{(M + m) g}}$

Solution:

$T = 2 π \sqrt{\frac{M}{k}} ∴ Mg = kl \Rightarrow k = \frac{Mg}{l} \Rightarrow T = 2 π \sqrt{\frac{(M + m) l}{Mg}}$

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