1. The rate of change of linear momentum of a body is called a:
Verification Matrix:
According to Newton's Second Law of Motion in terms of momentum, the applied force is directly equal to the time rate of change of linear momentum: $F = \frac{\Delta p}{\Delta t}$. Therefore, it represents (linear) force.
2. The term mass refers to the same physical concept as:
Verification Matrix:
Mass is an intrinsic quantitative measure of an object's inertia—its structural resistance to any alteration in its state of rest or uniform motion.
3. Which one of the following forces is also called a self-adjusting force?
Verification Matrix:
Static friction is called a self-adjusting force because its magnitude dynamically matches the applied external force up to its maximum limiting friction value ($f_s = F_{\text{applied}}$), preventing motion until broken.
4. The laws of motion show the relationship between:
Verification Matrix:
Newton’s laws fundamentally quantify dynamics by mapping how an external cause (force) produces a kinematic outcome (acceleration) acting on a given mass, concisely defined by $F = ma$.
5. The motion of a rocket in space is according to the law of conservation of:
Verification Matrix:
Rocket propulsion relies on backward exhaust emission. As high-velocity gas mass is ejected downward, an equal and opposite forward momentum is imparted to the rocket body, preserving the system's total linear momentum.
6. A bomb of mass $12\text{ kg}$ initially at rest explodes into two pieces of masses $4\text{ kg}$ and $8\text{ kg}$. The speed of the $8\text{ kg}$ mass is $6\text{ m/s}$. The kinetic energy of the $4\text{ kg}$ mass is:
Verification Matrix:
By conservation of momentum: $m_1 v_1 = m_2 v_2 \implies 4 \times v_1 = 8 \times 6 \implies v_1 = 12\text{ m/s}$. Now, evaluate the Kinetic Energy of the $4\text{ kg}$ mass: $K.E. = \frac{1}{2} m_1 v_1^2 = \frac{1}{2} (4) (12)^2 = 2 \times 144 = 288\text{ Joules}$.
7. If momentum is increased by $20\%$, then its $K.E.$ increases by:
Verification Matrix:
Kinetic energy relates to momentum via $K.E = \frac{p^2}{2m}$. If new momentum $p' = 1.2p$, then new kinetic energy $K.E' = \frac{(1.2p)^2}{2m} = 1.44 \times \left(\frac{p^2}{2m}\right) = 1.44 \cdot K.E$. An output scaling of $1.44$ indicates exactly a $44\%$ increase.
8. The kinetic energy of a body of mass $2\text{ kg}$ and momentum of $2\text{ N}\cdot\text{s}$ is:
Verification Matrix:
Using the dynamic relationship formula: $K.E. = \frac{p^2}{2m}$. Substituting the parameters gives $K.E. = \frac{2^2}{2(2)} = \frac{4}{4} = 1\text{ Joule}$.
9. For the same kinetic energy, the momentum is maximum for:
Verification Matrix:
Rearranging our work formula shows momentum is $p = \sqrt{2m(K.E.)}$. Given a fixed kinetic energy value, momentum scales directly with mass ($p \propto \sqrt{m}$). Since an alpha particle ($\text{He}^{2+}$) has the largest mass among the choices listed, it possesses the maximum momentum.
10. A $3\text{ kg}$ bowling ball experiences a net force of $15\text{ N}$. What will be its acceleration?
Verification Matrix:
Applying Newton's Second Law: $a = \frac{F}{m}$. Substituting values directly into the configuration yields $a = \frac{15\text{ N}}{3\text{ kg}} = 5\text{ m/s}^2$.
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