Daily Practice Questions

Explanation: The work done by the electric field equals the negative change in potential energy ($W = -\Delta U$). Since the shell has a positive charge $+Q$, it creates a positive electric potential at its center given by $V = kQ/R$. Moving a positive test charge $q$ from infinity (where potential is zero) to this point lowers the system's potential energy, meaning the electric field does positive work. However, the standard formula for work done *by* the field moving a like charge against repulsion from the surface to the center involves integrating the force; specifically, the potential difference is $V_f - V_i = kQ/R - 0$, so $\Delta U = q(kQ/R)$. The work done *by* the conservative electric field is $W = -\Delta U = -qkQ/R$. Note: Actually, for a positive shell and positive test charge, the force is repulsive. Moving from infinity to the center requires an external agent to do positive work, while the field does negative work because the displacement is opposite to the repulsive force direction. Thus, $W_{field} = -q(kQ/R)$. Wait, let's re-evaluate the physics carefully. Force on $q$ is repulsive (outward). Displacement is inward (from $\infty$ to $R$). Angle between Force and Displacement is $180^\circ$. Work = $\int \vec{F} \cdot d\vec{r} = F r \cos(180) < 0$. So work done *by the field* must be negative. Potential at center of shell ($r<R$): Inside a uniformly charged shell, $E=0$, so potential is constant and equals surface potential $V = kQ/R$. $\Delta U = q(V_f - V_i) = q(kQ/R - 0) = +kqQ/R$. $W_{field} = -\Delta U = -kqQ/R$. This matches choice (C). Corrected reasoning for the final output: The electric field inside a uniformly charged spherical shell is zero, so the electric potential is constant throughout the interior and equals the potential at the surface, $V = kQ/R$. The work done by the conservative electric field is equal to the negative change in potential energy ($W = -\Delta U

Explanation: According to the passage, Renoir was known for pushing boundaries and introducing fresh ideas into his artwork, whereas Daleur followed more conventional methods without notable innovation. Thus, Renoir’s work is characterized as highly innovative compared to Daleur’s.

Explanation: The correct answer is (B). This answer expresses the standard assumption involved in the sampling pattern. Nothing in the passage suggests that the households surveyed are representative of U.S. householders in general. Keep (B).

Explanation: The density of liquid water is greater than that of solid water, ice (ice floats!). The process of elimination could be used to answer this question even if you didn’t think of that right away. Because the temperature does not change during a phase change, the average kinetic energy of the particles in the substance undergoing the phase change is constant. Hydrogen bonds are broken during melting (and evaporation, see answer 272). According to conservation of energy, the potential energy must increase during melting and vaporization.

Explanation: The presence of glycolysis in the cytoplasm across all three domains provides strong evidence for a common ancestor because this metabolic pathway is ancient and highly conserved, suggesting it was present in the last universal common ancestor (LUCA). In contrast, membrane-bound organelles are absent in prokaryotes (Archaea and Bacteria), linear chromosomes are primarily found in eukaryotes while bacteria have circular ones, and introns are not universal across all domains. Therefore, only the universality of glycolysis supports a single shared origin for all life.

Explanation: Getting to the Answer: For −3, g (−3) = −3(−3) + 6 = 9 + 6 = 15. Choice (C) is correct.