Question

- S1 - CR
ULIV viru
ignment: Reflect on the Lab
Active
Comparing Densities
two balls have the same volume, but ball A has twice as much mass as ball B, which one will have the greater
ensity?
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?
two balls have the same mass, but ball P is twice as large as ball Q, which one will have the greater density?
ball X is twice as big as ball Y and weighs only half as much as ball Y, then which one will have the greater
ensity?

Answer 1

Part C.

Given:

Mass of ball P, Mp = mass of ball Q, MQ

Volume of P, Vp = 2 times volume of ball Q, 2VQ

Let's determine the ball with the greater density.

Apply the formula:

$\rho=\frac{m}{v}$

Now, for densities of both balls, we have:

$\begin{gathered} \rho_p=\frac{m_p}{v_p}=\frac{m_{}}{2v_Q} \\ \\ \rho_Q=\frac{m}{v_Q} \end{gathered}$

Now, divide density of P by density of Q:

$\begin{gathered} \frac{\rho_P}{\rho_Q}=\frac{\frac{m}{2v_Q}}{\frac{m}{v_Q}} \\ \\ =\frac{m}{2v_Q}*\frac{v_Q}{m} \\ \\ =\frac{1}{2} \end{gathered}$

Therefore, the density of ball P is 1/2 the density of the density of ball Q.

Hence, ball Q will have a greater density.

• (d). ,Given:

Volume of ball X = 2 * volume of ball Y

Mass of X = 1/2 * mass of ball Y.

We have:

$\begin{gathered} \rho_X=\frac{\frac{1}{2}m_Y}{2v_Y} \\ \\ \rho_Y=\frac{m_Y}{v_Y} \end{gathered}$

Divide density of ball X by that of ball Y:

$\begin{gathered} \frac{\rho_X}{\rho_Y}=\frac{\frac{\frac{1}{2}m_Y}{2v_Y}}{\frac{m_Y}{v_Y}} \\ \\ =\frac{\frac{1}{2}m_Y}{2v_Y}*\frac{v_Y}{m_Y} \\ \\ =\frac{1}{2}*\frac{1}{2} \\ \\ =\frac{1}{4} \end{gathered}$

Therefore, the density of ball X is 1/4 the density of ball Y.

Hence, ball Y will have the greater density.

ANSWER:

(c). Ball Q has the greater density

(d). Ball Y has the greater density