1. Work done by a centripetal force is always:
Verification Matrix:
Work is defined as $W = \vec{F} \cdot \vec{d} = Fd \cos\theta$. For uniform circular motion, the centripetal force acts radially inward toward the center, while the instantaneous displacement vector points along the tangent line of motion. Because they are perpendicular ($\theta = 90^\circ$) at every point, $\cos 90^\circ = 0$, making the work done exactly zero.
2. A body of mass $5\text{ kg}$ is moving with a momentum of $10\text{ kg}\cdot\text{m/s}$. A force of $0.2\text{ N}$ acts on it in the direction of motion of the body for $10\text{ seconds}$. The increase in kinetic energy is:
Verification Matrix:
1. Initial momentum $p_i = 10\text{ kg}\cdot\text{m/s}$. Initial kinetic energy: $K_i = \frac{p_i^2}{2m} = \frac{10^2}{2 \times 5} = 10\text{ J}$.2. Applied impulse: $\Delta p = F \cdot t = 0.2\text{ N} \times 10\text{ s} = 2\text{ kg}\cdot\text{m/s}$.
3. Final momentum: $p_f = p_i + \Delta p = 10 + 2 = 12\text{ kg}\cdot\text{m/s}$.
4. Final kinetic energy: $K_f = \frac{p_f^2}{2m} = \frac{12^2}{2 \times 5} = \frac{144}{10} = 14.4\text{ J}$.
5. Increase in kinetic energy: $\Delta K = K_f - K_i = 14.4\text{ J} - 10\text{ J} = 3.2\text{ J}$.
3. The kinetic energy of a light and a heavy object is the same. Which object has maximum momentum?
Verification Matrix:
The relationship between momentum ($p$) and kinetic energy ($K$) is $p = \sqrt{2mK}$. Given that $K$ is identical for both objects, momentum depends strictly on the square root of the mass ($p \propto \sqrt{m}$). Consequently, the heavy object ($m_{\text{heavy}} > m_{\text{light}}$) possesses greater momentum.
4. Two bodies of mass $1\text{ kg}$ and $2\text{ kg}$ have equal momentum. Then the ratio of their kinetic energies is:
Verification Matrix:
Using $K = \frac{p^2}{2m}$, when momentum ($p$) is constant, kinetic energy is inversely proportional to mass ($K \propto \frac{1}{m}$). Therefore, the ratio of their kinetic energies matches the inverse ratio of their masses: $\frac{K_1}{K_2} = \frac{m_2}{m_1} = \frac{2}{1}$, yields a ratio of $2:1$.
5. A body falls from a height $h$. After it has fallen a height $h/2$, it will possess:
Verification Matrix:
By the Law of Conservation of Mechanical Energy, the total mechanical energy is $E = U_i = mgh$. At the midpoint, the remaining height is $h/2$, making the remaining potential energy $U = mg(h/2) = \frac{1}{2}mgh$. The lost potential energy transforms fully into kinetic energy, meaning $K = E - U = mgh - \frac{1}{2}mgh = \frac{1}{2}mgh$. Thus, energy is split exactly half-and-half.
6. Which of the following quantities can be calculated by multiplying force and velocity?
Verification Matrix:
Power is defined as the rate of doing work: $P = \frac{\Delta W}{\Delta t} = \frac{\vec{F} \cdot \vec{d}}{\Delta t}$. Since average velocity is $\vec{v} = \frac{\vec{d}}{\Delta t}$, substitution yields the instantaneous formulation: $P = \vec{F} \cdot \vec{v}$.
7. The minimum velocity given to an object so that it emerges out from the gravitational field of earth is about:
Verification Matrix:
The escape velocity formula from Earth's surface is $v_{\text{esc}} = \sqrt{\frac{2GM_E}{R_E}} = \sqrt{2gR_E}$. Substituting real values ($g \approx 9.8\text{ m/s}^2$ and $R_E \approx 6.4 \times 10^6\text{ m}$) yields $v_{\text{esc}} \approx 11,200\text{ m/s} = 11.2\text{ km/s}$.
8. When one joule of work is done on a body in one second, the power of the body is said to be:
Verification Matrix:
By international standards definition, $1\text{ Watt}$ is exactly equal to an energy expenditure or work consumption profile rate of one joule per unit second ($1\text{ W} = 1\text{ J}/1\text{ s}$).
9. The absolute potential energy of an object depends on:
Verification Matrix:
Absolute gravitational potential energy relative to infinity is modeled by the equation $E_p = -\frac{GMm}{r}$. Since $r = R_E + h$, it is fundamentally determined by the mass ($m$) of the object and its absolute coordinate position/height ($h$) relative to the center of the attracting planet.
10. The escape velocity of a planet depends on which of the following factors?
Verification Matrix:
According to the escape velocity relation $v_{\text{esc}} = \sqrt{\frac{2GM}{R}}$, the minimum velocity depends on both the total mass ($M$) of the planet/star and its physical bounding radius ($R$). Crucially, it is completely independent of the test mass ($m$) of the departing vehicle or object itself.
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