Respuesta :
Answer:
Explanation:
To determine the unit of \( Y \), let's analyze the given expression:
\[ V = \sqrt{\frac{Y}{\text{density}}} \]
First, let's rearrange the equation to isolate \( Y \):
\[ V^2 = \frac{Y}{\text{density}} \]
\[ Y = V^2 \times \text{density} \]
Now, let's examine the units:
- The unit of \( V \) is typically meters per second (\( m/s \)).
- The unit of density depends on the context but is commonly expressed in kilograms per cubic meter (\( kg/m^3 \)).
So, the unit of \( Y \) will be:
\[ \text{Unit of } Y = (\text{Unit of } V)^2 \times (\text{Unit of density}) \]
Substituting the units:
\[ \text{Unit of } Y = (m/s)^2 \times (kg/m^3) \]
\[ \text{Unit of } Y = \frac{m^2}{s^2} \times \frac{kg}{m^3} \]
\[ \text{Unit of } Y = \frac{kg \cdot m}{s^2} \]
The unit of \( Y \) is kilograms times meters per second squared (\( kg \cdot m/s^2 \)), which is equivalent to the unit of force, also known as the newton (\( N \)). Therefore, the unit of \( Y \) is the newton (\( N \)).
