Physics 2018 Jamb Examination

In a block-and-tackle pulley system, the Velocity Ratio (V.R.) is equal to the total number of pulleys in both the fixed and movable blocks.
Total pulleys = 3 (fixed) + 2 (movable) = 5. Therefore, \( V.R. = 5 \).
Efficiency (\( \eta \)) is 72% or 0.72. We use the formula:\[ \eta = \frac{M.A.}{V.R.} \]\[ 0.72 = \frac{M.A.}{5} \]\[ M.A. = 0.72 \times 5 = 3.6 \]

An atom is electrically neutral when the number of protons equals the number of electrons. If an atom gains electrons, it becomes a negatively charged particle called an anion. If it loses electrons, it becomes a positively charged particle called a cation. Both of these charged species are broadly termed 'ions'.

Impulse is equal to the change in momentum. Since momentum is a vector, we must account for the change in direction.
Given:
Mass \( m = 800\text{g} = 0.8\text{kg} \)
Initial velocity \( u = 5\text{ms}^{-1} \)
Final velocity \( v = -5\text{ms}^{-1} \) (negative because it is in the opposite direction)

Calculation:\[ \text{Impulse} = m(v - u) \]\[ \text{Impulse} = 0.8(-5 - 5) \]\[ \text{Impulse} = 0.8(-10) = -8\text{kgms}^{-1} \]The magnitude of the impulse is 8\(\text{kgms}^{-1}\).

Forces of attraction between molecules are classified based on the types of molecules involved. Cohesive forces are the attractive forces between molecules of the same kind (e.g., water molecule to water molecule). Adhesive forces are the attractive forces between molecules of different kinds (e.g., water molecules to the molecules of a glass container).

Change in momentum (\( \Delta p \)) is calculated by considering the initial and final velocities as vectors.
Mass \( m = 100\text{g} = 0.1\text{kg} \)
Initial velocity \( u = 10\text{ms}^{-1} \)
Final velocity \( v = -2.0\text{ms}^{-1} \) (opposite direction)
\[ \Delta p = m(v - u) \]\[ \Delta p = 0.1(-2 - 10) \]\[ \Delta p = 0.1(-12) = -1.2\text{Ns} \]The magnitude of the change in momentum is 1.2Ns.

First, find the Velocity Ratio (V.R.) of the inclined plane:\[ V.R. = \frac{1}{\sin \theta} = \frac{1}{\sin 30^{\circ}} = \frac{1}{0.5} = 2 \]Next, find the Mechanical Advantage (M.A.) using the efficiency (\( \eta = 0.75 \)):\[ M.A. = \eta \times V.R. = 0.75 \times 2 = 1.5 \]Finally, find the effort (Force \( E \)) needed to pull the load (\( L = mg = 20 \times 10 = 200\text{N} \)):\[ M.A. = \frac{L}{E} \implies 1.5 = \frac{200}{E} \]\[ E = \frac{200}{1.5} = 133.3\text{N} \]

Inertia is the inherent property of a body that resists any change in its state of rest or uniform motion in a straight line. According to Newton's First Law of Motion, an object at rest will remain at rest unless acted upon by an external force; this 'laziness' or resistance to change is inertia.

First, we find the image distance (\( v \)) using the mirror formula:\[ \frac{1}{f} = \frac{1}{u} + \frac{1}{v} \]\[ \frac{1}{10} = \frac{1}{20} + \frac{1}{v} \implies \frac{1}{v} = \frac{1}{10} - \frac{1}{20} = \frac{2 - 1}{20} = \frac{1}{20} \]\[ v = 20\text{cm} \]Now, calculate linear magnification (\( M \)):\[ M = \frac{v}{u} = \frac{20}{20} = 1 \]When the object is placed at the center of curvature (\( u = 2f \)), the image is also formed at the center of curvature and is the same size as the object.

The electromotive force (e.m.f.) is the total work done by a source (like a battery) in moving a unit positive charge once around a complete circuit, including the internal parts of the source itself. Potential difference, on the other hand, is the work done moving a charge between two specific points in the circuit.

The moment of a force is defined as the product of the force and the perpendicular distance from the pivot to the line of action of the force. \[ \text{Moment} = \text{Force} \times \text{Perpendicular Distance} \]\[ \text{Moment} = 5\text{N} \times 0\text{m} = 0\text{Nm} \]