1. Tardigrade
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  3. Physics
  4. A spring balance has a scale that reads from 0 to 50 kg. The length of the scale is 20 cm. A block of mass m is suspended from this balance, when displaced and released, it oscillates with a period 0.5 s. The value of m is (Take g = 10 m s-2)

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Q. A spring balance has a scale that reads from $0$ to $50\, kg$. The length of the scale is $20\, cm$. A block of mass $m$ is suspended from this balance, when displaced and released, it oscillates with a period $0.5\, s$. The value of $m$ is (Take $g = 10 \,m \,s^{-2})$

Oscillations

Solution:

The $20\, cm$ length of the scaler reads upto $50 \,kg$.
$\therefore F= mg= (50 \,kg) (10\, m \,s^{-2}) = 500\, N$ and $x =20 \,cm = 0.2 \,m$
$\therefore $ Spring constant, $k = \frac{F}{x} = \frac{500\,N}{0.2\,m} $
$= 2500\,N\,m^{-1}$
As $T= 2\pi\sqrt{\frac{m}{k}} $
Squaring both sides, we get
$T^{2} = \frac{4\pi^{2}m}{k} $
$ m=\frac{T^{2}k}{4\pi^{2}} $
$=\frac{ \left(0.5\, s\right)^{2}\times\left(2500 \,N\, m^{-1}\right)}{4\times\left(3.14\right)^{2}}$
$= 16 \,kg$