Explanation

 Half-life definition:

The half-life of a radioactive substance is the time it takes for half of the atoms in a sample to decay. 

This decay process is inherent to the specific nucleus of the atom, meaning the half-life is a property of the substance itself and is independent of factors like the amount present or how old the sample is. 

Explanation

Soft iron is most suitable for transformer cores due to its high magnetic permeability and low hysteresis loss.

It allows efficient magnetic flux linkage, improving transformer performance.

Explanation

A body is in translational equilibrium when the vector sum of all forces acting on it is zero, meaning ∑F = 0.

This implies the sum of forces in both the x and y directions are also zero, i.e., ∑Fx = 0 and ∑Fy = 0.

The statement ∑τ = 0 is related to rotational equilibrium, not translational equilibrium.

The condition ∑β = 0 is not standard terminology in physics.

Explanation

Step 1: Use projectile motion

The maximum range of a projectile (ignoring air resistance) is given by:

R=v^2sin(2θ)/g​

The maximum range occurs when θ=45∘the value is maximum at (i.e.,sin(90∘)=1).

Step 2: Plug in values

• $v = 12 text{m/s}$

• g=10 m/s^2

R=12^2⋅1 ​/ 10 

= 144/10

​=14.4 meters

Explanation

According to Kirchhoff's law:

Coefficient of emission (e) + Coefficient of reflection (r) + Coefficient of transmission (t) = 1

Given: t = 0.33, r = 0.64

e + 0.64 + 0.33 = 1

e = 1 - 0.97

= 0.03

Explanation

Pressure is typically measured in units of force per unit area.

In the Imperial system, pressure is commonly measured in Pounds per Square Inch (PSI).

This is a widely used unit of pressure in engineering, physics, and many other fields.

Other common units of pressure include:

• Atmospheres (atm)
• Bars
• Pascals (Pa)
• Torr

Explanation

Gamma-ray cameras can observe radiations from the radioisotopes that are concentrated in the organs.

In medical imaging, radioisotopes are often used in nuclear medicine to diagnose and treat various conditions.

These isotopes emit gamma rays as they decay, and the gamma-ray camera detects these rays to create images of the organs where the isotopes have accumulated.

Explanation

For non-Ohmic materials, the current-voltage (I-V) relationship does not follow Ohm's law, which states that current is directly proportional to voltage (resulting in a linear I-V graph).

In non-Ohmic materials, the relationship between current and voltage is non-linear, and the I-V graph is typically curved.

Examples of non-Ohmic materials include diodes and transistors, where the resistance changes with voltage or current.

Explanation

A galvanometer is used as a null detector in a Wheatstone bridge.

It detects the zero current condition, indicating that the bridge is balanced.

Explanation

A common method of protection in a lighting circuit is to use a fuse.

It prevents damage by disconnecting the circuit if an overload or short circuit occurs.