I. In the Theorem of Pappus, the center of mass is always located inside the region or area of the figure.
II. In addition, the center of mass is always equal to the geometric centroid.
a. Both statements are true
b. Both statements are false
c. Statement I is true, the latter being false
d. Statement I is false, the latter being true
2. I. For springs obeying Hooke's Law, the work required to compress the material by dx distance is always less than the requirement to stretch it by the same dx distance.
II. The spring constant is dependent on the amount of force required to stretch it by some x distance.
a. Both statements are true
b. Both statements are false
c. Statement I is true, the latter being false
d. Statement I is false, the latter being true
3. I. As two objects move farther away from each other, the force of attraction between them decreases.
II. Thus, if the force of attraction decreases with distance, the work shall decrease as well.
a. Both statements are true
b. Both statements are false
c. Statement I is true, the latter being false
d. Statement I is false, the latter being true
4. I. For a positively charged q1 and negatively charged q2, the force will always be positive regardless of the signs.
II. Thus, in calculus, the signs of the charges do not affect the work or force between them.
a. Both statements are true
b. Both statements are false
c. Statement I is true, the latter being false
d. Statement I is false, the latter being true
5. I. In evaluating the moment of a planar lamina, a horizontal strip cannot be used as a representative area.
II. The moment of any planar lamina is the product of the mass of the region and its centroid.
a. Both statements are true
b. Both statements are false
c. Statement I is true, the latter being false
d. Statement I is false, the latter being true
6. I. For an object submerged in y distance from the water level, as y increases, the pressure experienced by the object decreases.
II. The same object placed in containers with three different areas submerging by the same depth will have a varying pressure depending on the containers.
a. Both statements are true
b. Both statements are false
c. Statement I is true, the latter being false
d. Statement I is false, the latter being true
7. I. The reaction kinetics of order 0 cannot be evaluated using the concept of integration.
II. If the order of reaction is 1 in PFR, given ?, and % conversion, the initial amount is not necessary to find ?.
a. Both statements are true
b. Both statements are false
c. Statement I is true, the latter being false
d. Statement I is false, the latter being true
8. I. In filtration using calculus, the fictitious volume (V) is considered a variable, like the filtrate (Q).
II. If the operation is a constant-rate process, the rate is always the ratio of the amount to be filtered and the time elapsed to obtain the necessary filtrate.
a. Both statements are true
b. Both statements are false
c. Statement I is true, the latter being false
d. Statement I is false, the latter being true
9. I. In a normal distribution curve, an average of 0 means that any value below 0 shall be located to its left.
II. Thus, scores within the 3ĂŹĆ’ to the left and right of the mean comprise at least 99% of the population's scores.
a. Both statements are true
b. Both statements are false
c. Statement I is true, the latter being false
d. Statement I is false, the latter being true
10. I. In the Cartesian coordinate plane, single integration produces an area under the curve (or between two curves).
II. In a three-dimensional system, single integration of an arc produces an area called the line integral.
a. Both statements are true
b. Both statements are false
c. Statement I is true, the latter being false
d. Statement I is false, the latter being true