Physics 2019 Jamb Examination

A wavefront is defined as the locus of points having the same phase: a line or surface on which the disturbance has the same value at all points. For example, the circular ripples on a pond represent wavefronts where all water particles at the crest are in the same phase of motion.

On a charged conductor, the surface charge density is highest at areas with the greatest curvature (the sharpest points). Point E is the sharpest point of the conductor.

The yield point is the stage in a stress-strain graph where the material transitions from elastic behavior to plastic behavior. At this point, the internal molecular structure begins to shift permanently, leading to a significant increase in extension even if the load is not increased substantially.

We solve this step-by-step from the middle out:
1. The parallel branch (2μF and 3μF): \( C_p = 2 + 4 = 6\mu\text{F} \).
2. Now we have four capacitors in series: 2μF, 3μF, 6μF (from step 1), and 4μF.
3. Use the series formula: \( \frac{1}{C_T} = \frac{1}{2} + \frac{1}{3} + \frac{1}{6} + \frac{1}{4} \).
4. Find a common denominator (12): \( \frac{1}{C_T} = \frac{6 + 4 + 2 + 3}{12} = \frac{15}{12} \).
5. \( C_T = \frac{4}{5} = 0.8 \mu\text{F} \).
 

We use the linear interpolation formula for thermometers:\[ \frac{\theta - 0}{100 - 0} = \frac{\text{Reading} - \text{LFP}}{\text{UFP} - \text{LFP}} \]\[ \frac{\theta}{100} = \frac{51 - 2}{100 - 2} \]\[ \frac{\theta}{100} = \frac{49}{98} \]\[ \frac{\theta}{100} = \frac{1}{2} \]\[ \theta = 50^\circ\text{C} \]

In uniform circular motion, the speed remains constant, but the velocity is constantly changing because the direction of motion is constantly changing. This change in direction constitutes an acceleration (centripetal acceleration) directed towards the center of the path.

According to Lenz's Law, the induced current will create a magnetic field that opposes the change causing it. If moving the coil *away* induces a current that creates a North pole facing the bar (to try and pull it back), and we look at the direction of current in the diagram (Right-Hand Grip Rule), we can determine the polarity. If the induced current creates an attraction to oppose the 'moving away,' and the bar is stationary, Y must be the opposite pole of what X produces. Based on standard physics problems of this type, Y is identified as a North pole.

Uniform velocity means the net force is zero, so the Pushing Force = Frictional Force (\( F_f \)).\[ F_f = 2000 \; \text{N} \]The Normal Reaction (\( R \)) equals the weight of the box:\[ R = mg = 500 \times 10 = 5000 \; \text{N} \] (using \( g=10 \; \text{m/s}^2 \))
The coefficient of friction \( \mu \) is:\[ \mu = \frac{F_f}{R} = \frac{2000}{5000} = 0.4 \]

Specific latent heat (\( L \)) is defined as the heat energy (\( Q \)) per unit mass (\( m \)) required to change the state of a substance without a change in temperature:\[ L = \frac{Q}{m} \]The SI unit for energy is the Joule (J) and for mass is the Kilogram (kg). Therefore, the unit is Joules per kilogram (\( \text{JKg}^{-1} \)).

Using the formula \( Q = mc\Delta\theta \), since \( Q \) is the same for both:\[ m_A c_A \Delta\theta_A = m_B c_B \Delta\theta_B \]Given:
\( \Delta\theta_A = 2\Delta\theta_B \)
\( m_A = \frac{1}{2}m_B \)
Substitute these into the equation:\[ (\frac{1}{2}m_B) c_A (2\Delta\theta_B) = m_B c_B \Delta\theta_B \]\[ (1) \cdot m_B c_A \Delta\theta_B = m_B c_B \Delta\theta_B \]Dividing both sides by \( m_B \Delta\theta_B \):\[ c_A = c_B \]The ratio is 1 : 1.