Certainly, let’s proceed step-by-step to solve these questions based on the given table of densities.
### Given Table of Densities:
[tex]\[
\begin{array}{|c|c|}
\hline \text{Substances} & \text{Density (gm/cm}^3\text{)} \\
\hline
X & 11 \\
\hline
Y & 8 \\
\hline
Z & 0.9 \\
\hline
\end{array}
\][/tex]
### i. समान पिण्ड भएका तीनैओटा मध्ये सबभन्दा कम आयतन कुन वस्तुको होला ? (Which substance will have least volume if equal masses of all are taken?)
For equal masses, the volume [tex]\( V \)[/tex] is inversely proportional to the density ([tex]\( \rho \)[/tex]). This means that a substance with a higher density will occupy less volume.
- Density of [tex]\( X \)[/tex]: [tex]\( 11 \, gm/cm^3 \)[/tex]
- Density of [tex]\( Y \)[/tex]: [tex]\( 8 \, gm/cm^3 \)[/tex]
- Density of [tex]\( Z \)[/tex]: [tex]\( 0.9 \, gm/cm^3 \)[/tex]
Among [tex]\( X, Y, \)[/tex] and [tex]\( Z \)[/tex], substance [tex]\( X \)[/tex] has the highest density ([tex]\( 11 \, gm/cm^3 \)[/tex]). Hence, substance [tex]\( X \)[/tex] will have the least volume when masses are equal.
Answer: The substance with the least volume for equal masses is [tex]\( \mathbf{X} \)[/tex].
### ii. समान आयतन भएका तीनैओटा मध्ये सबभन्दा कम पिण्ड कुन वस्तुको होला ? (Which substance will have the least mass if equal volume of all are taken?)
For equal volumes, the mass [tex]\( m \)[/tex] is directly proportional to the density ([tex]\( \rho \)[/tex]). This means that a substance with a lower density will have less mass.
- Density of [tex]\( X \)[/tex]: [tex]\( 11 \, gm/cm^3 \)[/tex]
- Density of [tex]\( Y \)[/tex]: [tex]\( 8 \, gm/cm^3 \)[/tex]
- Density of [tex]\( Z \)[/tex]: [tex]\( 0.9 \, gm/cm^3 \)[/tex]
Among [tex]\( X, Y, \)[/tex] and [tex]\( Z \)[/tex], substance [tex]\( Z \)[/tex] has the lowest density ([tex]\( 0.9 \, gm/cm^3 \)[/tex]). Hence, substance [tex]\( Z \)[/tex] will have the least mass when volumes are equal.
Answer: The substance with the least mass for equal volumes is [tex]\( \mathbf{Z} \)[/tex].
### iii. कुन वस्तु पानीमा उत्रिएला ? (Which one will float on water?)
A substance will float on water if its density is less than that of water. The density of water is [tex]\( 1 \, gm/cm^3 \)[/tex].
- Density of [tex]\( X \)[/tex]: [tex]\( 11 \, gm/cm^3 \)[/tex]
- Density of [tex]\( Y \)[/tex]: [tex]\( 8 \, gm/cm^3 \)[/tex]
- Density of [tex]\( Z \)[/tex]: [tex]\( 0.9 \, gm/cm^3 \)[/tex]
Among these substances, only [tex]\( Z \)[/tex] has a density less than water ([tex]\( 0.9 \, gm/cm^3 < 1 \, gm/cm^3 \)[/tex]). Hence, substance [tex]\( Z \)[/tex] will float on water.
Answer: The substance that will float on water is [tex]\( \mathbf{Z} \)[/tex].
### Summary of Answers:
1. Least volume for equal masses: [tex]\( \mathbf{X} \)[/tex]
2. Least mass for equal volumes: [tex]\( \mathbf{Z} \)[/tex]
3. Will float on water: [tex]\( \mathbf{Z} \)[/tex]
