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solniwko [45]
3 years ago
9

The density of diamond is 3.51 g/cm3 . the international (but non-si) unit for weighing diamonds is the "carat" (1 carat = 200 m

g exactly.) what is volume of a 0.87 carat diamond? answer in units of cm3 .
Physics
1 answer:
mixer [17]3 years ago
6 0

To calculate the volume of the diamond, we use the formula

\rho =\frac{m}{V}

Here, \rho is the density and its value given 3.51 g/cm^3

and m is mass and its value given0.87 carat.

1 carat = 200 mg = 0.200 g

So mass of the diamond, m= 0.87 carat \times 0.200 g/carat = 0.174 g

Substituting these values in above equation we get,

\rho =\frac{0.174 g}{3.51 g/cm^3} =0.0495 cm^3

Thus the volume of given carat diamond is 0.0495 cm^3.


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Where:

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y=V_{o}.t+\frac{1}{2}g.t^{2}    (3)

On the other hand, the maximum height  is accomplished when V=0:

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V_{o}-g.t=0    

V_{o}=g.t    (5)

Finding t:

t=\frac{V_{o}}{g}    (6)

Substituting (6) in (3):

y=V_{o}(\frac{V_{o}}{g})+\frac{1}{2}g(\frac{V_{o}}{g})^{2}    (7)

y_{max}=\frac{{V_{o}}^{2}}{2g}    (8)  Now we can calculate the maximum height of the rock

y_{max}=\frac{{(30m/s)}^{2}}{(2)(1.62m/s^{2})}   (9)

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y_{max}=277.777m  

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