To solve the problem of finding the pressure that a 7.5 kg block exerts on a tabletop, we'll break it down step by step.
1. Calculate the Force Exerted by the Block:
- The block's mass [tex]\( m \)[/tex] is 7.5 kg.
- The acceleration due to gravity [tex]\( g \)[/tex] is approximately 9.81 m/s².
- The force ([tex]\( F \)[/tex]) exerted by the block can be calculated using the formula:
[tex]\[
F = m \times g
\][/tex]
- Substituting the values:
[tex]\[
F = 7.5 \, \text{kg} \times 9.81 \, \text{m/s}^2 = 73.575 \, \text{N}
\][/tex]
2. Calculate the Pressure Exerted by the Block:
- The block’s bottom surface area [tex]\( A \)[/tex] is 0.6 m².
- Pressure ([tex]\( P \)[/tex]) is defined as force per unit area, which can be calculated using the formula:
[tex]\[
P = \frac{F}{A}
\][/tex]
- Substituting the values:
[tex]\[
P = \frac{73.575 \, \text{N}}{0.6 \, \text{m}^2} = 122.625 \, \text{Pa}
\][/tex]
Therefore, the pressure that the block exerts on the tabletop is approximately 122.625 Pa. Among the given options:
A. 73.5 Pa
B. 367.5 Pa
C. 226.5 Pa
D. 122.5 Pa
The closest and best answer is D. 122.5 Pa.
