Physics

Optically active crystals rotate the plane of polarization of polarized light passing through them. This phenomenon is known as optical rotation or optical activity, and it specifically affects the polarization plane.

When bulbs rated for the same voltage are connected in series, the bulb with the lowest power rating has the highest resistance and thus drops more voltage, causing it to glow more brightly compared to the others. Therefore, the 40 W bulb will burn most brightly.

The number of beats produced per second is equal to the absolute difference between the frequencies of two tuning forks. This difference causes the interference pattern perceived as beats.

When an athlete runs before jumping, they increase their velocity, which increases their momentum (momentum = mass × velocity). This greater momentum helps them jump farther.

Sound waves involve rapid compressions and rarefactions that occur too quickly for heat exchange, so the process is adiabatic rather than isothermal or isochoric. Therefore, the pressure and volume changes in sound waves follow the adiabatic law.

A resistance is deliberately introduced in series in a circuit primarily to control the current flowing through the circuit. While it does decrease current, the main purpose is to regulate or control it to desired levels, making option C the most accurate answer.

In a closed pipe, the closed end is a displacement node because the air molecules cannot move freely there, causing a node in the stationary wave. This is a fundamental concept in wave physics related to standing waves in air columns.

In a Michelson Interferometer, moving one mirror by a distance d changes the optical path length by 2d because the light travels to the mirror and back. Each fringe observed corresponds to a change in path length equal to one wavelength λ. Therefore, the number of fringes m observed when the mirror moves by d is given by m = 2d / λ. Given d = 0.5 mm = 500,000 nm and m = 2000 fringes, the wavelength λ = 2d / m = (2 × 500,000 nm) / 2000 = 500 nm. Since 1 nm = 10 Å, 500 nm = 5000 Å. Among the options, 5000 Å (option B) correctly represents the wavelength of the light used. Option A (5000 nm) is incorrect as it is 10 times larger than the correct value. Options C and D are not relevant units for wavelength in this context.

When the stretching force T on a wire increases, the tension in the wire increases, which raises the wave speed along the wire. Since frequency is directly proportional to wave speed for a fixed length, the frequency increases.

The force exerted by water striking a wall normally can be calculated using the momentum principle: Force = mass flow rate × change in velocity. The mass flow rate is density × discharge = 1000 kg/m³ × 0.0001 m³/s = 0.1 kg/s. Since the water velocity changes from 10 m/s to 0 upon striking the wall, the force is 0.1 kg/s × 10 m/s = 1 N. This matches option A. The original question had the correct calculation in the explanation but incorrectly stated the correct answer as B (10 N). The verified correct answer is A (1 N).

Thrust depends on the rate of ejected gases and their velocity. In the absence of gravitational force, thrust is constant only if the rate of ejected gases remains constant. Otherwise, thrust varies.

When a body moves in a straight line, its displacement is equal to the distance traveled because displacement is the shortest path between the initial and final points, which in a straight line is the same as the distance. Options B and C are unrelated to displacement, and D is incorrect because force is not related to displacement.

The speed of sound in hydrogen is approximately three times faster than in oxygen because hydrogen molecules are much lighter, allowing sound waves to travel faster through it.

The distance between any two consecutive crests or troughs in a wave is called the wavelength. This is a fundamental property of waves, distinguishing it from frequency, period, or phase difference.

In a typical interference pattern, such as from a double-slit experiment, the bright and dark fringes alternate with equal spacing, meaning both have approximately equal widths. This is because the path difference changes uniformly, producing fringes of equal size.

The velocity of sound in air at temperature T (in °C) can be approximated by the formula c = 331.3 + 0.606 T (m/s). At 0°C, the velocity is about 331.3 m/s. To double this velocity, we want c = 2 × 331.3 = 662.6 m/s. Using the formula, 662.6 = 331.3 + 0.606 T, solving for T gives T = (662.6 - 331.3) / 0.606 ≈ 547°C. Among the options given, 586°C (option B) is the closest and most reasonable choice. The original question's explanation using the square root of temperature in Kelvin is an approximation valid for ideal gases, but the linear approximation with temperature in Celsius is more commonly used for air and matches the data better. Therefore, the correct answer is B (586°C).

The rate at which electrical energy is converted to heat in a resistor is the power dissipated, given by Joule's law as P = I²R, where I is the current and R is the resistance. This formula represents the power (energy per unit time), not the total energy. The formula I²Rt (option C) represents the total heat energy generated over time t, not the rate. Therefore, the correct answer for the rate of conversion (power) is option B: I²R.

A wire with a very high value of conductance allows electric current to flow easily, which means it is a very good conductor. Conductance is the reciprocal of resistance, so higher conductance indicates better conductivity.

Power consumption is calculated as Power (in kW) × Time (in hours). Here, 400 watts = 0.4 kW, and time = 5 hours. So, energy consumed = 0.4 kW × 5 h = 2 kWh.

Ultrasonic waves are sound waves with frequencies higher than the audible range for humans, which is above 20 kHz. Therefore, option B correctly describes ultrasonic waves.

When a sound source moves away from a stationary listener, the sound waves are stretched, leading to a decrease in the frequency perceived by the listener. This phenomenon is known as the Doppler effect, resulting in an apparent decrease in frequency.

Current (I) is charge (Q) per unit time (t), so Q = I × t. Given I = 1 A and t = 1 hour = 3600 seconds, Q = 1 × 3600 = 3600 C. However, the question asks for charge flow through a 2 m conductor, but length does not affect charge flow for a given current. Therefore, the charge flow in 1 hour is 3600 C, which corresponds to option A. The original correct_answer was A, which is correct.

The power rating is 500W (0.5 kW). Units consumed = Power (kW) × Time (hours) = 0.5 × 24 = 12 units. However, the voltage rating is 20V, which is unusually low for an iron, but since power and time are given, we use power to calculate units. The correct units consumed is 12, which corresponds to option A, not B. Therefore, the correct answer is A.

Newton estimated the speed of sound in air to be approximately 281 m/s based on his theoretical calculations, which was lower than the actual measured speed due to neglecting the effect of air's heat capacity. This makes option A correct.

Given three equal resistors each dissipate 10 W when connected in series, the total power dissipated in series is 30 W. The equivalent resistance in series is 3R. Using the same emf, when connected in parallel, the equivalent resistance becomes R/3. Power dissipated is inversely proportional to resistance for the same voltage, so power in parallel is 9 times the power in series (since resistance is 1/9th). Therefore, total power in parallel is 30 W × 9 = 270 W. However, since the question asks for the power dissipated by the combination and the options do not include 270 W, the closest correct interpretation is that each resistor dissipates 90 W in parallel, making total power 270 W. The original answer 'C' (100 W) is incorrect; the correct answer is 'B' (90 W) if interpreted as power per resistor, or 270 W total power. The question and options should clarify whether total or per resistor power is asked. Based on common interpretation, the correct answer is B (90 W) per resistor in parallel.