Question

q13. which of the following statement is true about the objects shown below? a and b have the same volume a and b have the same density a and b have the same mass

Explanation:

Step1: Count the number of circles in each object

Object A has 9 circles, object B has 16 circles. Assuming each circle has the same volume, mass and density (since they seem to be identical - looking), volume \(V = n\times V_{1}\) (where \(n\) is the number of circles and \(V_{1}\) is the volume of one - circle), mass \(m=n\times m_{1}\) (where \(m_{1}\) is the mass of one circle), and density \(
ho=\frac{m}{V}\).
Since \(n_{A}
eq n_{B}\), \(V_{A}
eq V_{B}\) and \(m_{A}
eq m_{B}\). But if the material of each circle is the same, \(
ho_{A}=
ho_{B}\) because \(
ho_{A}=\frac{m_{A}}{V_{A}}=\frac{n_{A}m_{1}}{n_{A}V_{1}}=\frac{m_{1}}{V_{1}}\) and \(
ho_{B}=\frac{m_{B}}{V_{B}}=\frac{n_{B}m_{1}}{n_{B}V_{1}}=\frac{m_{1}}{V_{1}}\).

Answer:

A and B have the same density