Physics

Albert A. Michelson is credited with the most accurate early measurements of the speed of light using precise interferometry techniques, making option B correct.

The standard value for solar irradiance at the Earth's surface on a clear day at noon is approximately 1.4 kW/m², which is the closest to the correct scientific value among the options provided.

When unpolarized light passes through a Polaroid filter, it becomes plane polarized because the Polaroid only allows light waves oscillating in one plane to pass through.

Geothermal energy originates from multiple sources within the Earth. The primary contributors are: (A) the decay of radioactive elements such as uranium, thorium, and potassium isotopes, which produce significant heat; (B) the compression of material in the Earth, including frictional heating and phase changes as the core solidifies; and (C) the residual heat from the Earth's original formation and accretion. Together, these processes contribute to the Earth's internal heat that drives geothermal energy. Therefore, the most accurate answer is (D) All of the above (A, B, and C).

Centripetal force acts perpendicular to the direction of the particle's instantaneous velocity, so it does no work on the particle as work requires a component of force along the displacement.

The cutoff frequency (also called the -3dB frequency) of an RC circuit is given by the formula f = 1/(2πRC). Among the given options, the closest correct formula is 1/(2RC), which is option D. The exact formula includes 2π in the denominator, so none of the options perfectly match the exact formula, but option D is the closest and most correct approximation compared to the others.

The signs of the rectangular components (x and y) of a vector depend on the quadrant in which the vector lies. In the 1st quadrant, both x and y components are positive, so they have the same sign. In the 3rd quadrant, both x and y components are negative, so they also have the same sign. Therefore, the two rectangular components of a vector have the same sign in both the 1st and 3rd quadrants. Since option C states 'Both 1st and 3rd', it is the correct answer. The question asks for the quadrant(s) where the components have the same sign, and both these quadrants satisfy that condition.

The root mean square (r.m.s) value of an alternating current is defined as the square root of the mean (average) of the square of the instantaneous current values over one complete cycle. This matches option B.

The permeability of free space (also called the magnetic constant) is exactly 4π × 10⁻⁷ henry per meter (H/m), which is equivalent to Wb·A⁻¹·m⁻¹ in SI units. This value is fundamental in electromagnetism.

Magnetic flux (Φ) is defined as the product of the magnetic flux density (B) and the area (A) through which the field lines pass, so Φ = B × A. This relationship directly connects the two quantities.

The vectors î, ĵ, and k̂ are the standard unit vectors in Cartesian coordinates. The cross product ĵ × k̂ equals î, and the dot product î · î is 1, so the magnitude of î · (ĵ × k̂) is 1.

Electromagnetic waves carry energy as they propagate through space. They also carry momentum, but the primary and most direct transport property is energy. They do not carry mass or heat themselves.

An ammeter is connected in series with the circuit so that it measures the total current flowing through that part of the circuit. Connecting it in parallel would not measure the total current and could damage the meter.

The root mean square (r.m.s) current is defined as the steady current that produces the same heating effect in a resistor as the alternating current. This is because the r.m.s value represents the effective value of the AC current in terms of power dissipation.

A voltmeter is designed to measure the potential difference (voltage) across two points without drawing any significant current from the circuit, ensuring accurate voltage measurement. Other instruments like ammeters draw current, and galvanometers measure current, while CROs display voltage waveforms but are not primarily used to measure potential without current draw.

For three coplanar forces to keep a body in equilibrium, they must be concurrent, meaning their lines of action intersect at a single point. This ensures the net force and net moment are zero, satisfying equilibrium conditions.

In a multi-range ammeter, the meter movement has a fixed full-scale deflection current and internal resistance. To measure higher currents (increase the range), shunt resistors are connected in parallel with the meter coil to bypass most of the current. As the range increases, the shunt resistor value decreases to allow more current to bypass the meter coil, protecting it from damage. Therefore, the shunt value decreases as the range increases.

The sensitivity of a moving coil galvanometer is increased by increasing the number of turns in the coil, which increases the magnetic torque for a given current, thereby producing a larger deflection. While a stronger magnetic field also affects sensitivity, increasing the number of turns is a more direct and commonly used method.

Torque and energy both have the same dimensional formula M L² T⁻². Momentum and impulse both have dimensions M L T⁻¹. Energy and work have identical dimensions M L² T⁻². Mass has dimension M, while moment of inertia has dimension M L². Therefore, the pair that does not have identical dimensions is mass and moment of inertia, making option D the correct answer.

The torque $\tau$ on a rectangular coil carrying current $I$ with $N$ turns, area $A$, in a magnetic field $B$ is given by $\tau =NIAB\sin \varphi$, where $\varphi$ is the angle between the normal to the plane of the coil and the magnetic field. When the plane of the coil is parallel to the magnetic field, the normal to the coil is perpendicular to the field, so $\varphi ={90}^{\circ }$ and $\sin {90}^{\circ }=1$. Thus, the torque is maximum and equals $\tau =NIAB$. The formula involving cosine is incorrect for torque; it is the sine of the angle that determines the torque magnitude. Therefore, the correct general formula is $\tau =NIAB\sin \varphi$ (option B).

The direction of the vector (cross) product is determined by the right-hand rule, which states that if you point your right hand's fingers along the first vector and curl them towards the second vector, your thumb points in the direction of the cross product.

In a pure resistor circuit, the voltage and current are in phase, meaning they have zero phase difference. This means the voltage and current reach their maximum and zero values simultaneously.

A galvanometer is designed to be very sensitive to small currents, which is achieved by having very low damping. Low damping allows the coil to deflect easily in response to current without quickly losing energy to resistive forces.

A central force acts along the line joining the centers of two bodies and therefore cannot produce torque about the center of force, as torque requires a force component perpendicular to the radius vector.

A Wheatstone bridge is balanced when there is no potential difference across the galvanometer branch, resulting in zero current flow through it. This condition allows accurate measurement of unknown resistance.