Question

A piece of silver has a cavity inside it. The mass of silver in air is 367.5gm. and that in water is 315gm.
If the density of silver is 10.5gm/cc, find the volume of the cavity.

PLEASE GIVE ME THE CORRECT ANSWER

Answer 1

Given:

A piece of silver has a cavity inside it. The mass of silver in air is 367.5 gm. and that in water is 315 gm.  If the density of silver is 10.5 gm/cc.

To Find:

What is the volume of cavity?

Solution:

Let us take:

Volume of silver = V  cm³

Volume of cavity = u    cm³

Mass of silver in air (M) = 367.5 gm

$\mathbf{\textrm{Density of silver}=10.5 \ \ \ \dfrac{g}{cm^{3}}}$

Volume of silver can be find out from this formula:

$\mathbf{\textrm{Volume of silver}=\dfrac{Mass\ of\ silver\ in\ air}{Density\ of\ Silver}}$

$\mathbf{\textrm{Volume of silver}=\dfrac{367.5}{10.5}}$

Volume of silver = V= 35  cm³

Volume of cavity can be find out from this formula:

$\mathbf{W_{w}=W_{a}-F_{BS}-F_{BC}}$      ...1)

$\mathbf{Weight\ in\ water =W_{w}= 315 g}$

$\mathbf{Weight\ in\ air =W_{a}= 367.5 g}$

$\mathbf{Buoyant\ force\ due\ to\ silver\ volume=F_{BS}=\rho_{w} \times Volume\ of\ silver\times g}$$\mathbf{Take\ density\ of\ water=\rho _{w}= 1 \ \ \dfrac{g}{cm^{3}}}$

$\mathbf{Buoyant\ force\ due\ to\ silver\ volume=F_{BS}=1\times 35\times g=35g}$

$\mathbf{Buoyant\ force\ due\ to\ cavity\ volume=F_{BC}=\rho_{w} \times Volume\ of\ cavity\times g}$$\mathbf{Take\ density\ of\ water=\rho _{w}= 1 \ \ \dfrac{g}{cm^{3}}}$$\mathbf{Buoyant\ force\ due\ to\ cavity\ volume=F_{BC}=1\times u\times g=u\times g}$

From equation 1):

$\mathbf{W_{w}=W_{a}-F_{BS}-F_{BC}}$

$\mathbf{315g=367.5g-35g-u\times g}$

On simplify, we get:

u = 17.5 cm³

Means volume of cavity is 17.5 cm³

Answer 2

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Means volume of cavity is 17.5 cm³