Explanation

esistance R of a conductor is given by:

R = ρ (L / A)  

Where:  

- ρ = resistivity  

- L = length  

- A = cross-sectional area

If length (L) is made 4 times, and area and material stay the same, then:

R becomes 4 × original resistance

Explanation

According to Lenz's Law, the induced current always flows in such a direction that it opposes the change causing it.

- As the loop moves toward the magnet, the magnetic flux through it increases.

- The induced current creates a magnetic field that opposes the magnet’s field, resisting the motion.

Explanation

- Terminal voltage (V) of a cell is given by:  

  V = EMF − Ir,  

  where I = current, r = internal resistance.

- When no current flows (I = 0),  

  V = EMF (since Ir = 0).

Explanation

- Mechanical waves (like sound) need a medium (solid, liquid, or gas) to propagate.

- In outer space, which is a vacuum, there are no particles to transmit vibrations.

Explanation

- Gamma rays have the highest frequency and shortest wavelength in the electromagnetic spectrum.

- This gives them the greatest energy and strongest penetrating power.

- They are used in cancer treatment and come from radioactive decay.

Explanation

Thus, the First law of thermodynamics furnishes the relationship between:

• heat
• work
• the internal energy of the system

Explanation

The total energy E in simple harmonic motion (SHM) is given by:

E = (1/2) k A²

Where:  

- k is the spring constant  

- A is the amplitude

This indicates that energy is proportional to the square of the amplitude.  

Frequency and time period do not affect total energy (though they relate to speed), and wavelength is not relevant in SHM (it applies to waves).

Explanation

Protons repel each other due to their positive charges (electromagnetic force), but the strong nuclear force binds them tightly inside the nucleus, overcoming this repulsion.

Explanation

The electric field E due to an infinite charged sheet is given by:

E = σ / (2ε₀)

Where:  

- σ = surface charge density  

- ε₀ = permittivity of free space

Since E is directly proportional to σ, if the surface charge density increases by 25%, the electric field also increases by 25%.

Explanation

According to the principle of continuity for incompressible fluids:

A₁v₁ = A₂v₂

Where:  

- A = cross-sectional area  

- v = fluid speed

When the pipe becomes narrower (A decreases), the fluid speed (v) must increase to keep A × v (volume flow rate) and hence mass flow rate constant