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kramer
3 years ago
9

If ball C is 3 times the volume of ball D and ball D has 1/3 the mass of ball C, which has the greater density?

Physics
1 answer:
Alex Ar [27]3 years ago
6 0

Answer:

They have same density

Explanation:

The density of an object is defined as

d=\frac{m}{V}

where

m is the mass of the object

V is its volume

Let's call m_c and V_c the mass and the volume of ball C, respectively. Therefore, the density of ball C is:

d_c = \frac{m_c}{V_c}

We know that the volume of ball C is 3 times the volume of ball D, so

V_c = 3 V_d \rightarrow V_d = \frac{V_c}{3}

And we also know that ball D has 1/3 the mass of ball C:

m_d = \frac{m_c}{3}

So, the density of ball D is:

v_d = \frac{m_d}{V_d}=\frac{m_c/3}{V_d/3}=\frac{m_c}{V_c}=d_c

Therefore, the two balls have same density.

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