Physics

Newton's first law of motion states that an object will remain at rest or in uniform motion unless acted upon by an external force, which is the concept of inertia.

Displacement is the shortest straight-line distance between the initial and final positions, while distance is the total path length traveled. Since displacement cannot exceed the total distance traveled, the ratio of displacement to distance can never be greater than one.

When an electron and a positron annihilate, they typically produce two gamma-ray photons to conserve both energy and momentum. This is the most common and fundamental annihilation process.

A rainbow is formed because water droplets in the atmosphere act like prisms, refracting, dispersing, and reflecting sunlight to create the spectrum of colors seen.

In three-dimensional space, a vector is represented by three components corresponding to the x, y, and z axes. Therefore, a vector can have a maximum of three components in space.

Graphite is a good neutron moderator because it slows down fast neutrons effectively without capturing them, which is essential in nuclear reactors. Helium is a gas and not used as a moderator, cadmium is a strong neutron absorber (poison), and ordinary water absorbs more neutrons than graphite, making graphite preferable in some reactor designs.

In beta decay, a neutron in the nucleus transforms into a proton or vice versa, emitting a beta particle (electron or positron) and an antineutrino or neutrino. Thus, the neutrino (or antineutrino) is produced alongside the daughter nucleus and beta particle.

The relativistic mass m_rel of an object moving at speed v is given by m_rel = m_0 / sqrt(1 - v^2/c^2), where m_0 is the rest mass and c is the speed of light. To find the speed at which the relativistic mass doubles, set m_rel = 2 m_0, which gives 2 = 1 / sqrt(1 - v^2/c^2). Solving for v yields v = sqrt(3)/2 * c ≈ 0.866 c. Since the speed of light c ≈ 3.0 × 10^8 m/s, the speed at which the relativistic mass doubles is approximately 2.6 × 10^8 m/s. This matches option B exactly, confirming it as the correct answer.

The coefficient of linear expansion (α) is defined as the fractional change in length per unit temperature change, which is mathematically expressed as ΔL divided by (L times ΔT), or ΔL/(LΔT).

Newton's first law of motion states that an object remains at rest or in uniform motion unless acted upon by an external force. This law holds true only in inertial frames of reference, where no acceleration is present.