Question

A spiral spring of natural length 20.00cm has a scale
pan hanging on its lower end while the other end is
fixed firmly to a support.When an object of mass 50g
is placed in the pan, the length of the spring becomes
22.00 cm.When another object of mass 70g is placed in
The pan, the length becomes 22.25cm Calculate the
mass of the scale pan. (g = 10m/s]​

Answer 1

The  mass of the scale pan : 0.11 kg

Further explanation

Given

A spiral spring's length = 20 cm

mass 50 g ⇒ the length = 22 cm

mass 70 g ⇒ the length = 22.25 cm

Required

the  mass of the scale pan

Solution

Hooke's Law :

$\tt F=k.\Delta x$

The spring constant (k) :

$\tt k=\dfrac{\Delta F}{\Delta x}=\dfrac{g.(70-50)}{22.25-22}=\dfrac{g.20}{0.25}=g.80~g/cm=10~m/s^2\times 8~kg/m=80~N/m$

mass of the scale pan=m(for 50 g mass) :

$\tt (m+0.05).g=80\times (0.22-0.20)\\\\m=0.11~kg$