RRB JE Physics Questions with Detailed Solutions

The correct answer is (D) 1 Ω

Explanation:
• The resistance (R) of a wire is directly proportional to its length (L) and inversely proportional to its cross-sectional area (A).
• The formula is: R = ρ(L/A), where ρ (rho) is the resistivity of the material.
• For the first wire: R₁ = ρ(L/A) = 9 Ω.
• For the second wire, the material is the same, so ρ is constant. The new length is L/3, and the new area is 3A.
• R₂ = ρ * ((L/3) / (3A)) = ρ * (L / 9A) = (1/9) * ρ(L/A).
• Since ρ(L/A) is 9 Ω, R₂ = (1/9) * 9 Ω = 1 Ω.

Information Booster:
• Resistivity (ρ): Resistivity is an intrinsic property of the material and does not change when the physical dimensions (length or area) change, as long as temperature remains constant.
• Thick vs. Thin wires: Thicker wires (larger Area) have lower resistance, much like a wider pipe allows more water to flow easily. Shorter wires also have lower resistance.
• Wire Stretching: If a wire is *stretched* to 3 times its length, its area automatically becomes 1/3rd to conserve volume. In that case, the resistance would become 9 times the original.

Additional Knowledge:
• Options A, B, and C: These are common mathematical errors arising from incorrectly applying the fractions in the denominator or failing to account for both the change in length and area simultaneously.

The correct answer is (D) Potential energy decreases while kinetic energy increases, maintaining constant total mechanical energy.

Explanation:
• During free fall, an object moves downwards towards the Earth. As its height decreases, its gravitational potential energy (mgh) decreases.
• Simultaneously, its velocity increases due to gravitational acceleration, leading to a proportional increase in kinetic energy (½mv²).
• According to the Law of Conservation of Energy, in a closed system (ignoring air resistance), the total mechanical energy (Potential Energy + Kinetic Energy) remains absolutely constant throughout the fall.

Information Booster:
• Terminal Velocity: If air resistance is considered, the object eventually stops accelerating and reaches terminal velocity. At this point, kinetic energy becomes constant, and the lost potential energy is converted into thermal energy (heat).
• Highest Point: At the highest point before falling, an object has maximum potential energy and zero kinetic energy.
• Just Before Impact: Just before hitting the ground, the object has maximum kinetic energy and zero potential energy (relative to the ground).

Additional Knowledge:
• Option A: They do not remain constant; energy is actively changing forms.
• Option B: Energy cannot be destroyed. If one decreases, another must increase.
• Option C: In true "free fall" (which implies a vacuum), there is no air friction to generate heat energy.

The correct answer is (D) Stars would not twinkle; their light would remain steady.

Explanation:
• The twinkling of stars (stellar scintillation) is entirely an optical illusion created by Earth's atmosphere.
• Starlight travels across vast distances through the vacuum of space undisturbed. However, once it hits Earth's atmosphere, it passes through layers of air with varying temperatures and densities (and thus varying refractive indices).
• These shifting layers constantly bend (refract) the pinpoint of starlight in random directions. The amount of light reaching our eye fluctuates rapidly, making the star appear to twinkle. Without an atmosphere to cause this refraction, the light would hit our eyes continuously and steadily.

Information Booster:
• Why planets don't twinkle: Planets are much closer to Earth and appear as extended light sources (a disk) rather than points. The atmospheric fluctuations across the different points of the disk cancel each other out, yielding a steady glow.
• Delayed Sunset and Early Sunrise: Atmospheric refraction is also responsible for the sun appearing about 2 minutes before the actual sunrise and remaining visible for 2 minutes after actual sunset.
• Space Telescopes: This is precisely why telescopes like Hubble and James Webb are placed in space—to avoid the "blurring" and "twinkling" caused by atmospheric refraction.

Additional Knowledge:
• Option A (Color change): Color is determined by the star's surface temperature, not refraction (though extreme refraction near the horizon can cause brief colorful flashes, the primary effect is steadiness).
• Option B (Disappear): Without an atmosphere, stars would actually appear brighter and clearer.
• Option C (Planets would twinkle): Planets already don't twinkle, and removing refraction wouldn't make them start.

The correct answer is (A) The passenger tends to remain at rest while the car moves forward, showing inertia.

Explanation:
• According to Newton's First Law of Motion, an object at rest stays at rest, and an object in motion stays in motion with the same speed and in the same direction unless acted upon by an unbalanced force.
• When a car suddenly starts moving forward, the lower part of the passenger's body moves with the car due to contact with the seat.
• However, the upper part of the body tends to remain in its state of rest due to inertia. This resistance to change in motion causes the passenger to feel a backward jerk.

Information Booster:
• Inertia of Rest: The inherent property of an object to resist any change in its state of rest. Examples include shaking a branch to make fruits fall or beating a carpet to remove dust.
• Inertia of Motion: The resistance to change in a state of uniform motion, which is why passengers fall forward when a moving bus brakes suddenly.
• Mass and Inertia: The mass of an object is a quantitative measure of its inertia; heavier objects have greater inertia.

Additional Knowledge:
• Friction from the seat (Option B): Friction actually helps pull the lower body forward with the car; it does not cause the backward jerk of the upper body.
• Pushed backward by air (Option C): Air resistance inside the cabin is negligible in this context and is not responsible for the physical jerk.
• Seat pushes the passenger forward (Option D): While the seat pushes the lower body forward, the sensation of falling backward is purely due to the upper body's inertia of rest.

The correct answer is (D) The potential energy is halved

Explanation:
• Gravitational potential energy (PE) is the energy stored in an object due to its vertical position or height.
• The mathematical formula for potential energy is PE = mgh, where 'm' is mass, 'g' is acceleration due to gravity, and 'h' is the height above the reference point.
• Since PE is directly proportional to mass, if the mass 'm' is reduced to half (m/2) while keeping 'g' and 'h' constant, the new potential energy becomes (m/2)*g*h, which is exactly half of the original PE.

Information Booster:
• Direct Proportionality: The formula PE = mgh shows that potential energy increases linearly with both mass and height. Double the height, and you double the PE.
• Work-Energy Theorem: The potential energy of an object at a certain height is exactly equal to the work done against gravity (Work = Force x Displacement = mg x h) to lift it to that height.
• Zero Potential Energy: Potential energy is relative. An object lying on the ground has zero gravitational potential energy relative to the ground because its height (h) is zero.

Additional Knowledge:
• Option A (Becomes zero): Potential energy would only become zero if the height became zero (object is placed on the ground).
• Option B (Doubled): This would occur if the mass or the height were multiplied by two.
• Option C (Unchanged): This would only happen if any change in mass was perfectly offset by an inverse change in height.

The correct answer is (A) The potential energy doubles

Explanation:
• Gravitational potential energy (PE) is the energy an object possesses due to its vertical position or height in a gravitational field.
• The mathematical formula is: PE = m × g × h (where m = mass, g = acceleration due to gravity, and h = height).
• Since the mass and gravity remain constant, the potential energy is directly proportional to the height (PE ∝ h).
• By raising the shelf from 2 meters to 4 meters, the height (h) is exactly doubled. Therefore, the potential energy must also exactly double.

Information Booster:
• Reference Point: Potential energy is relative. It is always measured with respect to a chosen base level (usually the ground, where h = 0 and PE = 0).
• Path Independence: The work done against gravity (and thus the PE gained) depends only on the initial and final height, independent of the path taken to raise the object.
• Conservation of Energy: If the object falls from the 4m shelf, this accumulated potential energy converts continuously into kinetic energy until it hits the ground.

Additional Knowledge:
• Halves (Option C): This would only happen if the height was reduced by half (e.g., dropping from 4m to 2m).
• Remains the same (Option B): Height dictates PE; PE cannot remain unchanged if the height changes, assuming the object's mass hasn't vanished.

The correct answer is (D) It provides a low-resistance path for leakage current

Explanation:
• Domestic appliances like refrigerators, electric irons, and microwaves often have metallic bodies. If insulation fails, the live wire can touch this metallic casing, making it electrically "live."
• The earth wire connects the metallic casing of the appliance directly to a metal plate buried deep in the earth.
• Because the earth wire offers exceptionally low electrical resistance, any leakage or fault current instantly flows through it to the ground rather than passing through the body of a human user touching the appliance, thereby preventing a fatal electric shock.

Information Booster:
• Triggering the Fuse/MCB: When a massive fault current flows through the earth wire to the ground, it usually exceeds the circuit's rated capacity, instantly blowing the fuse or tripping the Miniature Circuit Breaker (MCB) and isolating the appliance.
• Color Coding: In modern electrical wiring color codes, the earth wire is typically insulated with a green or green-and-yellow striped plastic cover.
• The Three Wires: A standard domestic circuit consists of three wires: Live (carries voltage), Neutral (completes the circuit), and Earth (safety measure).

Additional Knowledge:
• Controls current flow (Option A): Current flow in normal operation is controlled by switches and the resistance of the appliance, not the earth wire.
• Prevents fuse melting (Option B): Incorrect. In fact, a severe leakage to earth is exactly what *causes* the fuse to melt or the MCB to trip to disconnect the circuit safely.
• Increases appliance voltage (Option C): The earth wire has absolutely no role in stepping up or modifying the supply voltage.

The correct answer is (D) 25 m/s

Explanation:
• The ball is dropped from rest, so its initial velocity (u) = 0 m/s. It accelerates downwards due to gravity (a = 10 m/s²) for a time (t) of 5 seconds.
• First, find the final velocity (v) right before hitting the ground using the equation of motion: v = u + at.
• v = 0 + (10 × 5) = 50 m/s.
• For an object undergoing uniform acceleration, average speed is calculated as: (Initial Velocity + Final Velocity) / 2.
• Average Speed = (0 + 50) / 2 = 25 m/s.

Information Booster:
• Alternative Method using Distance: You can calculate the height it fell from using s = ut + ½at². s = 0 + ½(10)(5²) = 125 meters.
• Average speed is total distance / total time: 125m / 5s = 25 m/s.
• Free Fall: The motion of the dropped ball is a classic example of free fall, where gravity is the sole force acting on the body (assuming negligible air resistance).

Additional Knowledge:
• 50 m/s (Option C): This is the *final* maximum speed at the exact moment of impact, not the average speed over the entire 5-second journey.
• 10 m/s (Option B): This is the acceleration rate (10 m/s²), mistakenly selected as a speed metric.

The correct answer is (A) The bulb's filament reaches a higher temperature, emitting visible light

Explanation:
• According to Joule's Law of Heating, both devices generate heat due to electrical resistance.
• An incandescent bulb uses a tungsten filament, which has a very high melting point (approx 3380°C). When current flows, it gets heated to around 2500°C, causing it to become incandescent and emit visible light.
• A room heater uses a nichrome wire element. It heats up to a lower temperature (around 900°C to 1000°C), primarily emitting infrared radiation (heat) with very little to a dull red glow in the visible spectrum.

Information Booster:
• Incandescence: The emission of light from a hot body as a result of its high temperature.
• Tungsten: Preferred for bulb filaments due to its high resistivity and exceptionally high melting point, preventing it from melting at white-hot temperatures.
• Nichrome: An alloy of nickel, chromium, and iron used in heating elements because it does not oxidize (burn) easily at high temperatures.

Additional Knowledge:
• Magnetic effect (Option B): Incorrect, as both operate on the heating effect of electric current, not the magnetic effect.
• Different material (Option C): While true that they use different materials (tungsten vs nichrome), this option is incomplete without mentioning the resulting temperature difference that actually causes the light emission.
• Circuit design (Option D): The fundamental reason is the temperature threshold for incandescence, not the overall circuit layout.

The correct answer is (D) Convex mirror using the mirror formula for virtual, diminished images

Explanation:
• A convex mirror is a spherical mirror with an outwardly curved reflecting surface.
• Regardless of where an object is placed in front of a convex mirror, it always produces an image that is virtual, erect (upright), and diminished (smaller than the object).
• Because the images are diminished, the mirror can pack a much wider field of view into a small surface area, making it perfect for surveillance in stores and as rear-view mirrors in vehicles.

Information Booster:
• Mirror Formula: 1/f = 1/v + 1/u. For a convex mirror, the focal length (f) is always positive.
• Magnification: The magnification (m) of a convex mirror is always positive (indicating an erect image) and less than 1 (indicating a diminished image).
• Diverging Mirror: A convex mirror is also known as a diverging mirror because it scatters parallel rays of light outward.

Additional Knowledge:
• Plane mirror (Option A): Produces images of the exact same size and offers a very limited field of view, making it useless for store surveillance.
• Concave mirror (Options B and C): A concave mirror generally forms real, inverted images. It only forms upright images when the object is very close (between the pole and focus), but that image is highly magnified, not diminished. It does not provide a wide field of view.

The correct answer is (C) It bends towards the normal

Explanation:
• This phenomenon is governed by the laws of refraction. Light travels faster in a rare medium (air) and slower in a denser medium (glass).
• When a light ray strikes the air-glass interface obliquely, one side of the wavefront enters the glass and slows down before the other side. This uneven slowing causes the entire ray to pivot.
• The fundamental rule is: When light travels from an optically rarer medium (air) to an optically denser medium (glass), it bends towards the imaginary line perpendicular to the surface (the normal).

Information Booster:
• Snell's Law: This bending is mathematically quantified by Snell's Law (sin i / sin r = constant), where the constant is the refractive index of the glass relative to air.
• The Second Interface: When the light eventually exits the glass slab and re-enters the air (denser to rarer), it speeds back up and bends away from the normal.
• Lateral Displacement: Because the two interfaces of a rectangular glass slab are parallel, the emergent ray is parallel to the incident ray but is shifted sideways. This shift is called lateral displacement.

Additional Knowledge:
• Bends away (Option A): This would happen if the light were entering from glass to air (dense to rare).
• Travels straight (Option B): This only occurs if the light ray hits the glass at an exactly 90-degree angle (normal incidence), not obliquely.
• Reflected back (Option D): While a tiny fraction of light reflects (partial reflection), the bulk of the ray refracts and enters the glass.

The correct answer is (D) Stars would not twinkle; their light would remain steady.

Explanation:
• The twinkling of stars is fundamentally a phenomenon caused by atmospheric refraction.
• Starlight must pass through multiple layers of Earth's atmosphere, which have varying optical densities due to temperature and pressure differences.
• These shifting layers constantly bend (refract) the starlight in different directions. This continuous shifting causes the apparent brightness of the star to fluctuate, creating the twinkling effect.
• Without Earth's atmosphere, or if it lacked these varying densities, the path of light would be perfectly straight, and the stars would appear as steady points of light, exactly as they look to astronauts in space.

Information Booster:
• Planets vs. Stars: Planets generally do not twinkle because they are much closer to Earth. They appear as extended disks of light rather than point sources. The slight shifts in light rays from different parts of the planet's disk cancel each other out, maintaining a steady glow.
• Advanced Position: Atmospheric refraction also causes stars and the sun to appear slightly higher in the sky than their actual geometric position.

Additional Knowledge:
• Color change (Option A): While scintillation can cause slight color shifts, steady light is the primary consequence of removing refraction.
• Disappearance (Option B): The absence of an atmosphere would make stars brighter and clearer, not invisible.
• Planets twinkling (Option C): Removing refraction would prevent all celestial bodies from twinkling, not induce it in planets.

The correct answer is (A) A battery creates a potential difference that sets electrons in motion

Explanation:
• In a disconnected metallic wire, free electrons are present, but they move completely randomly due to thermal energy. Because this movement is random, there is no net flow of charge in any specific direction, so there is no electric current.
• A battery functions as a pump for electrons. When connected across the ends of the wire, the chemical reactions inside the battery create a potential difference (voltage).
• This potential difference establishes an electric field inside the wire, exerting a force on the negatively charged electrons, compelling them to drift in a single direction (from the negative terminal to the positive terminal). This coordinated flow constitutes an electric current.

Information Booster:
• Water Analogy: Think of a water pipe lying flat on the ground; water won't flow until one end is lifted higher than the other (creating a pressure/potential difference). A battery does exactly this for electricity.
• Drift Velocity: The average velocity with which free electrons get drifted towards the positive end of the conductor under the influence of an external electric field is called drift velocity.

Additional Knowledge:
• Gravity (Option B): The mass of an electron is so infinitesimally small (9.1 × 10^-31 kg) that gravity has practically zero effect on setting up an electrical current.
• Copper (Option C): Being copper means it has free electrons (it's a good conductor), but without a "push" (voltage), they won't form a current.
• Intrinsic energy (Option D): Thermal energy causes random motion, not the unidirectional motion required for current.

The correct answer is (D) 1 Ω

Explanation:
• The resistance (R) of a wire is directly proportional to its length (l) and inversely proportional to its cross-sectional area (A). The formula is R = ρ × (l / A), where ρ (rho) is the resistivity of the material.
• For the first wire, we are given: R1 = ρ × (l / A) = 9 Ω.
• For the second wire, it is made of the "same material", so its resistivity (ρ) is the same. Its new length is l' = l/3, and its new area is A' = 3A.
• Let's calculate the new resistance: R2 = ρ × (l' / A')
• R2 = ρ × [ (l/3) / (3A) ]
• R2 = ρ × (l / 9A) = (1/9) × [ρ × (l / A)]
• Since ρ × (l / A) = 9, substitute that in: R2 = (1/9) × 9 = 1 Ω.

Information Booster:
• Resistivity Factor: Resistivity (ρ) is an intrinsic property of a material. It only changes if the material itself changes or if the temperature changes. It does not change with length or thickness.
• Real-world Application: Thick, short copper cables are used to connect car batteries to the starter motor because they offer extremely low resistance, allowing the massive surge of current required to turn the engine.

Additional Knowledge:
• By shortening the wire to a third, you reduce resistance by a factor of 3. By making it three times thicker, you reduce resistance by another factor of 3. Total reduction factor = 3 × 3 = 9. So, 9 / 9 = 1.

The correct answer is (A) ₹360

Explanation:
• First, we find the electrical energy consumed per day. Energy (E) = Power (P) × Time (t).
• The power rating is 500 W, which is equal to 0.5 kW (since 1000 W = 1 kW).
• Energy consumed in one day = 0.5 kW × 6 hours = 3 kWh (kilowatt-hours).
• Over a period of 30 days, the total energy consumed = 3 kWh/day × 30 days = 90 kWh.
• The cost per unit (1 kWh) is given as ₹4.00.
• Therefore, the total cost = 90 kWh × ₹4.00/kWh = ₹360.

Information Booster:
• Commercial Unit of Energy: The kilowatt-hour (kWh) is the commercial unit of electrical energy, often simply referred to as a "unit" on electricity bills.
• Joule Conversion: 1 kWh is equivalent to 3.6 × 10^6 Joules (3.6 million Joules) of energy.

Additional Knowledge:
• Common Mistake: If one forgets to convert Watts to Kilowatts, they might calculate 500 × 6 × 30 = 90,000, leading to mathematical confusion. Always ensure Power is in kW and Time is in Hours before multiplying for commercial costing.