Class 11 Physics: Golden Numericals

Soumya Sir's Physics Class GOLDEN NUMERICALS Class 11 High-Probability Problems

1. The "Maximum Range" ⭐⭐⭐⭐⭐

"A ball is thrown at 30°. Find max height & range..."

Formulas:
$R = \frac{u^2 \sin 2\theta}{g}$
$H = \frac{u^2 \sin^2 \theta}{2g}$
Trick: Max Range is at 45°. At this angle, $R = 4H$.

2. The "Connected Motion" ⭐⭐⭐⭐

"Two masses m1 and m2 connected by pulley..."

Logic: Draw FBD for each mass.
Shortcut Formula:
Acceleration: $a = \frac{(m_2 - m_1)g}{m_1 + m_2}$
Tension: $T = \frac{2m_1m_2g}{m_1 + m_2}$

3. The "Safe Turn" ⭐⭐⭐⭐⭐

"Find max speed on a banked curve with friction..."

The Monster Formula:
$v_{max} = \sqrt{Rg \left(\frac{\tan\theta + \mu}{1 - \mu\tan\theta}\right)}$
Tip: If friction is zero ($\mu=0$), formula becomes $v = \sqrt{Rg \tan\theta}$.

4. The "Spring Compression" ⭐⭐⭐

"Block hits a spring. Find max compression..."

Concept: Conservation of Energy.
Kinetic Energy Lost = Spring Potential Energy Gained.
$\frac{1}{2}mv^2 = \frac{1}{2}kx^2$

5. Carnot Engine ⭐⭐⭐⭐

"Efficiency is 50%. Sink temp reduced by 50K..."

The Trap: Temperatures MUST be in KELVIN ($^\circ C + 273$).
Formula:
$\eta = 1 - \frac{T_{sink}}{T_{source}}$

6. The "Organ Pipe" ⭐⭐⭐

"Find the ratio of frequencies in Open vs Closed pipe..."

Open Pipe: All harmonics (1:2:3...). Fundamental $\nu = v/2L$.
Closed Pipe: Only Odd (1:3:5...). Fundamental $\nu = v/4L$.

7. Terminal Velocity (Fluids) ⭐⭐⭐⭐

Scenario: Small ball dropping in viscous liquid.
Logic: Weight = Upthrust + Viscous Drag.
Formula: $v_t = \frac{2}{9} \frac{r^2 (\rho - \sigma)g}{\eta}$
Memorize the relationship: $v_t \propto r^2$. (If radius doubles, speed becomes 4 times).

Always Draw FBD First!
FBD = Free Body Diagram.

Prepared by Soumya Sir