A mass is suspended from a spring having spring constant ' K ' is… - Vidyadip

MCQ

A mass is suspended from a spring having spring constant ' $K$ ' is displaced vertically and released, oscillates with period ' $T$ '. The weight of the mass suspended is ( $g=$ gravitational acceleration)

A
$\frac{K T g}{4 \pi^2}$
✓
$\frac{K T^2 g}{4 \pi^2}$
C
$\frac{K T g}{2 \pi^2}$
D
$\frac{K T^2 g}{2 \pi^2}$

✓

Answer

Correct option: B.

$\frac{K T^2 g}{4 \pi^2}$

(b) : Time period of spring - block system is given by $T=2 \pi \sqrt{\frac{M}{K}}$
Squaring both sides, we get
$
T^2=4 \pi^2 \frac{M}{K} ; M=\frac{K T^2}{4 \pi^2}
$
Weight of mass suspended, $W=M g$
$
W=\frac{K T^2 g}{4 \pi^2}
$

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