Physics

When the same current passes through wires of different thickness, the thinner wire has higher resistance, causing more heat to be produced in it according to Joule's law (heat produced ∝ resistance × current² × time).

The acceleration of a rocket at any instant is directly proportional to the velocity of the expelled gases (exhaust velocity). This is derived from the rocket thrust equation and Newton's second law. The acceleration a = F/m = (ṁ · vₑ)/m, where ṁ is the mass flow rate of the expelled gases, vₑ is the exhaust velocity, and m is the rocket's instantaneous mass. Thus, acceleration is proportional to the first power (n = 1) of the velocity of the expelled gases, not inversely proportional.

The elastic modulus (Young's modulus) has the same dimensions as pressure or stress, which is force per unit area. Force has dimensions MLT^-2, and area has dimensions L^2, so the dimension of elastic modulus is ML^-1T^-2.

The reciprocal of resistivity is called conductivity, which measures how well a material allows the flow of electric current. Resistivity and conductivity are inversely related physical properties.

Electrical energy is measured in kilowatt-hours (kWh), which represents the amount of energy consumed when one kilowatt of power is used for one hour. The other options are units of power or incorrect terms.

Adding wax to the prong of a tuning fork increases its mass, which lowers its natural frequency, causing the frequency to decrease.

Sound travels fastest in solids because particles are more closely packed, allowing vibrations to transfer more quickly. Among the given options, copper is a solid and thus has the greatest velocity of sound compared to water (liquid), air, and ammonia (gases).

In a vibrating cord, points where the amplitude is maximum are called antinodes because these are the points of maximum displacement in a standing wave. Nodes are points of zero amplitude, while troughs and crests refer to wave features but not specifically to standing wave amplitude maxima.

For projectile motion at the same initial speed, the ranges at complementary angles (30° and 60°) are equal because the range formula depends on sin(2θ), and sin(60°) = sin(120°), making their ranges equal.

Polarization is a property unique to transverse waves, as it involves the orientation of oscillations perpendicular to the direction of wave propagation. Longitudinal waves cannot be polarized because their oscillations are parallel to the direction of propagation, allowing us to distinguish between the two types of waves using polarization.

When the crest of one wave coincides with the trough of another, their amplitudes subtract, resulting in a decrease in overall amplitude. This phenomenon is called destructive interference.

Longitudinal waves, such as sound waves, do not exhibit polarization because their particle displacement is parallel to the direction of wave propagation, unlike transverse waves where polarization occurs due to perpendicular oscillations.

The speed of stationary waves on a stretched string depends on the tension in the string and the linear mass density, but it is independent of the number of loops (harmonics) and the point where the string is plucked. Therefore, options A and C do not affect the wave speed, making D the correct answer.

Waves transmit energy from one place to another without the transfer of mass. The particles of the medium oscillate around their equilibrium positions but do not travel with the wave.

The frequency of light remains constant when it passes from one medium to another, while velocity, wavelength, and amplitude can change depending on the medium's properties.

Thermocouples work by converting heat energy directly into electrical energy through the Seebeck effect, where a temperature difference between two different metals produces a voltage.

In plane polarized light, the vibrations of the electric field occur in a single plane perpendicular to the direction of propagation. This means the vibration direction is perpendicular to the light's travel direction, making option C correct.

The human ear is most sensitive to sounds in the frequency range of approximately 2000 to 4000 hertz, which corresponds to the frequencies where speech sounds are concentrated and where hearing sensitivity peaks.

For bulbs rated at the same voltage, higher wattage means higher power consumption and thus lower resistance, since Power = Voltage² / Resistance. Therefore, the 200 watt bulb has less resistance than the 100 watt, 300 watt, or 60 watt bulbs at the same voltage.

When two bodies move toward each other, their relative speed is the sum of their speeds, which equals 6 m/s. When they move in the same direction, the relative speed is the difference of their speeds, which equals 4 m/s. Solving these equations: x + y = 6 and x - y = 4 gives speeds 5 m/s and 1 m/s.

The resistance of a metallic wire increases with temperature because the atoms vibrate more at higher temperatures, causing more collisions for the electrons and thus increasing resistance.

Sound waves are longitudinal mechanical waves and cannot be polarized because their oscillations occur in the direction of propagation. In contrast, radio waves, ultraviolet rays, and X-rays are electromagnetic waves and can be polarized.

A point source of light in a homogeneous medium emits light equally in all directions, producing a spherical wave front as the wave propagates outward uniformly.

When white light is used in Young's double slit experiment, the different wavelengths interfere to produce colored fringes due to the superposition of various colors, resulting in a spectrum of colors in the interference pattern.

Newton's 2nd law of motion states that force is equal to mass times acceleration (F = ma), thus it defines the relationship between both force and acceleration, not just acceleration alone.