Explanation

The motion of a free-falling object can be described by Newton's second law of motion,

force (F) = mass (m) times acceleration (a)

Newton's second law of motion states that F = ma, or net force is equal to mass times acceleration.

The other name for Newton's second law is the law of force and acceleration.

Explanation

Wave theory cannot explain why electrons are ejected instantly and depend on light frequency, not intensity.

It is explained only by particle (photon) nature of light.

Explanation

In Fraunhofer diffraction, the screen is placed far away (or lens used) so that incoming and outgoing waves are plane.

It is the most common type studied for single-slit and double-slit diffraction patterns.

Explanation

Explanation

A source of 1 kW power working for 1 hour does:

Work done = Power × Time = 1kW × 1hour = 1kWh

This is the standard unit of electrical energy.

Explanation

1 volt is defined as: 1V = 1J/1C

It means when 1 joule of work is done to move 1 coulomb of charge between two points, the potential difference is 1 volt.

Explanation

In circular motion, the inward (centripetal) force is: F = mv²/r

Hence, the force is directly proportional to the square of the speed of the stone.

Explanation

Kinetic energy is a scalar (depends only on magnitude, no direction).

Momentum is a vector (has both magnitude and direction).

Explanation

The problem says:

• Body starts from rest ($u=0$)

• Moves with an acceleration $a$ (value not given)

• After $t=3$ sec, momentum $p=mv$

• Velocity after 3 sec: $v=u+at=0+a\times 3=3a$

• Momentum $p=m\times 3a=3ma$

Explanation

When a metal sheet is inserted between the plates of a parallel plate capacitor, it effectively splits the capacitor into two capacitors in series.

Given:

• Distance between plates = $d$

• Metal sheet thickness = $\frac{d}{2}$

• Air gaps on each side of the sheet = $\frac{d}{4}$ each (since metal is conductor, field exists only in the gaps).

Original capacitance:

$$\mathrm{<b><font\; color="\#0000ff">C</font></b>}<b><font\; color="\#0000ff">=</font></b>\frac{{\mathrm{<b><font\; color="\#0000ff">\epsilon </font></b>}}_{\mathrm{<b><font\; color="\#0000ff">0</font></b>}}\mathrm{<b><font\; color="\#0000ff">A</font></b>}}{\mathrm{<b><font\; color="\#0000ff">d</font></b>}}$$

After insertion:
Each air gap capacitance:

$${\mathrm{<b><font\; color="\#0000ff">C</font></b>}}_{\mathrm{<b><font\; color="\#0000ff">1</font></b>}}<b><font\; color="\#0000ff">=</font></b>{\mathrm{<b><font\; color="\#0000ff">C</font></b>}}_{\mathrm{<b><font\; color="\#0000ff">2</font></b>}}<b><font\; color="\#0000ff">=</font></b>\frac{{\mathrm{<b><font\; color="\#0000ff">\epsilon </font></b>}}_{\mathrm{<b><font\; color="\#0000ff">0</font></b>}}\mathrm{<b><font\; color="\#0000ff">A</font></b>}}{\mathrm{<b><font\; color="\#0000ff">d</font></b>}\mathrm{<b><font\; color="\#0000ff">/</font></b>}\mathrm{<b><font\; color="\#0000ff">4</font></b>}}<b><font\; color="\#0000ff">=</font></b>\frac{\mathrm{<b><font\; color="\#0000ff">4</font></b>}{\mathrm{<b><font\; color="\#0000ff">\epsilon </font></b>}}_{\mathrm{<b><font\; color="\#0000ff">0</font></b>}}\mathrm{<b><font\; color="\#0000ff">A</font></b>}}{\mathrm{<b><font\; color="\#0000ff">d</font></b>}}<b><font\; color="\#0000ff">=</font></b>\mathrm{<b><font\; color="\#0000ff">4</font></b>}\mathrm{<b><font\; color="\#0000ff">C</font></b>}$$

These two are in series:

$$\frac{\mathrm{<b><font\; color="\#0000ff">1</font></b>}}{{\mathrm{<b><font\; color="\#0000ff">C</font></b>}}_{\mathrm{<b><font\; color="\#0000ff">t</font></b>}\mathrm{<b><font\; color="\#0000ff">o</font></b>}\mathrm{<b><font\; color="\#0000ff">t</font></b>}\mathrm{<b><font\; color="\#0000ff">a</font></b>}\mathrm{<b><font\; color="\#0000ff">l</font></b>}}}<b><font\; color="\#0000ff">=</font></b>\frac{\mathrm{<b><font\; color="\#0000ff">1</font></b>}}{\mathrm{<b><font\; color="\#0000ff">4</font></b>}\mathrm{<b><font\; color="\#0000ff">C</font></b>}}<b><font\; color="\#0000ff">+</font></b>\frac{\mathrm{<b><font\; color="\#0000ff">1</font></b>}}{\mathrm{<b><font\; color="\#0000ff">4</font></b>}\mathrm{<b><font\; color="\#0000ff">C</font></b>}}<b><font\; color="\#0000ff">=</font></b>\frac{\mathrm{<b><font\; color="\#0000ff">2</font></b>}}{\mathrm{<b><font\; color="\#0000ff">4</font></b>}\mathrm{<b><font\; color="\#0000ff">C</font></b>}}<b><font\; color="\#0000ff">=</font></b>\frac{\mathrm{<b><font\; color="\#0000ff">1</font></b>}}{\mathrm{<b><font\; color="\#0000ff">2</font></b>}\mathrm{<b><font\; color="\#0000ff">C</font></b>}}$$$${\mathrm{<b><font\; color="\#0000ff">C</font></b>}}_{\mathrm{<b><font\; color="\#0000ff">t</font></b>}\mathrm{<b><font\; color="\#0000ff">o</font></b>}\mathrm{<b><font\; color="\#0000ff">t</font></b>}\mathrm{<b><font\; color="\#0000ff">a</font></b>}\mathrm{<b><font\; color="\#0000ff">l</font></b>}}<b><font\; color="\#0000ff">=</font></b>\mathrm{<b><font\; color="\#0000ff">2</font></b>}\mathrm{<b><font\; color="\#0000ff">C</font></b>}$$