Sure, let's break it down step by step:
1. Understand the given values:
- Mass of the object: [tex]\( 25 \)[/tex] hectograms (hg)
- Velocity of the object: [tex]\( 5 \)[/tex] meters per second (m/s)
- Radius of the circular path: [tex]\( 5 \)[/tex] meters (m)
2. Convert the mass into kilograms (kg):
- We need to convert the mass from hectograms to kilograms because the standard SI unit for mass is kilograms.
- 1 hectogram is equivalent to 0.1 kilogram.
- Therefore, [tex]\( 25 \)[/tex] hectograms is equal to [tex]\( 25 \times 0.1 = 2.5 \)[/tex] kilograms.
3. Recall the formula for centripetal acceleration:
- The centripetal acceleration [tex]\( a_c \)[/tex] of an object moving in a circular path is given by the formula:
[tex]\[
a_c = \frac{v^2}{r}
\][/tex]
where [tex]\( v \)[/tex] is the velocity and [tex]\( r \)[/tex] is the radius of the circular path.
4. Substitute the known values into the formula:
- Velocity [tex]\( v = 5 \)[/tex] m/s
- Radius [tex]\( r = 5 \)[/tex] m
- Substitute these values into the formula:
[tex]\[
a_c = \frac{(5)^2}{5}
\][/tex]
5. Perform the calculation:
- Calculate the velocity squared:
[tex]\[
5^2 = 25
\][/tex]
- Divide by the radius:
[tex]\[
a_c = \frac{25}{5} = 5 \, \text{m/s}^2
\][/tex]
6. Conclusion:
- The centripetal acceleration of the object is [tex]\( 5 \)[/tex] meters per second squared ([tex]\( \text{m/s}^2 \)[/tex]).
So, to summarize, the mass of the object in kilograms is [tex]\( 2.5 \, \text{kg} \)[/tex], the velocity is [tex]\( 5 \, \text{m/s} \)[/tex], the radius is [tex]\( 5 \, \text{m} \)[/tex], and the centripetal acceleration calculated is [tex]\( 5.0 \, \text{m/s}^2 \)[/tex].
