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Momentum Conservation in Collision?
A 5 kg particle is moving with a velocity of 2 m/s east collides with a 3 kg particle moving west at 3 m/s. If the collision is perfectly inelastic, calculate the final velocity of the combined mass and explain the change in the total linear momentum.
Induction's Time-Space Tradeoff?
A physicist is designing a device to generate a magnetic field that induces an electromotive force (EMF) in a conductor attached to a rotating wheel. If the wheel completes a full rotation in 4 seconds and induces a maximum EMF of 12 V, at what distance from the center of the wheel would the conductor be placed to achieve a maximum EMF, assuming the magnetic field's strength is directly proportional to the distance?
Resistance and Temperature?
A copper wire is connected between a variable power source and an ammeter. If the temperature of the wire is increased by 10°C, by how much percentage will the resistance of the wire increase, assuming the wire is initially at a temperature of 20°C? Use the formula for temperature dependence of resistance and justify your answer.
Combination of Capacitors?
Three capacitors of capacitances 2 μF, 3 μF and 5 μF are connected in parallel across a 20 V battery. How will the total capacitance of the combination be affected if a dielectric material of dielectric constant 3 is inserted between the plates of the 2 μF capacitor?
Work Done by a Variable Force?
A block of mass 2 kg is moved from x = 0 to x = 4 m along a straight line against a variable force F(x) = 3x N. Assuming the block starts from rest, calculate the total work done on the block by the force F(x). Explain your answer in the context of the block's kinetic energy at the end of the displacement.
Resistance in a Wire Network?
A wire of resistance R1 is connected in series with another wire of resistance R2. The total resistance of the network is measured to be 6 ohms when a voltmeter is connected across R2. If the voltage applied is 12 volts, find the value of R2.
Calculating Power Consumption?
A 100 W electric bulb is used for 6 hours a day. If the cost of electricity is ₹ 3 per unit, calculate the daily cost of using this bulb and suggest ways to reduce the cost.
Induced Currents in Moving Conductors?
A wire loop is placed inside a moving magnet and connected to a sensitive ammeter. Suddenly, the magnet is removed, and the loop is rotated while moving with uniform speed. Describe the changes in the ammeter reading and explain the underlying phenomenon using the concept of electromagnetic induction.
Comparing Resistances in Parallel
Consider a circuit with three identical resistors connected in parallel, each of resistance 2 ohms. If a voltage source of 6 volts is connected across the circuit, compare the total resistance of the circuit with the resistance of a single resistor, and explain the reasoning behind your answer.
A Vehicle Saves Energy
A car travels 60 km/h on a highway when its engine speed is 1500 rpm. Then it enters a hilly section where it climbs a 10 m high slope. If the car's engine speed drops to 800 rpm, calculate the work done against gravity in either case and explain why the car saves energy when climbing the hill.
Magnetic Field and its Effects?
A bar magnet is placed inside a hollow copper tube. Explain the observed phenomena when the tube is rotated slowly around its axis while the magnet is stationary. Assume the tube is insulated from the ground.
A Spherical Conductor Holds Charge?
A spherical conductor of radius 5 cm has a charge of 0.5 μC distributed uniformly over its surface. Does this conductor behave as an equipotential surface everywhere inside and outside, and what does this imply about its electrostatic potential?
Hill Climbing: Efficient Path?
A cyclist is climbing a hill with a slope of 1 in 5. The cyclist can either take the steeper, shorter path or the gentler, longer path. Compare the work done by the cyclist in both cases, considering the force applied and the distance travelled.
Roller Coaster Physics?
A roller coaster car of mass 2000 kg moves in a vertical circle of radius 20 m with a speed of 12 m/s. If the track is banked at an angle of 30°, determine the normal force acting on the car at the topmost point of the circle.
Inducing a Change?
In a generator, a 300-turn copper coil with a radius of 0.1 m is placed in a uniform magnetic field of 2 T. If the coil is rotated at a frequency of 50 Hz, determine the magnitude and direction of the induced EMF. Assume the plane of the coil coil is initially perpendicular to the magnetic field.
Magnetic Field of a Current Carrying Loop?
A circular loop of copper wire carrying a current of 2A is placed in a vertical plane. If the radius of the loop is 0.5m, describe the direction and magnitude of the magnetic field at the centre of the loop, considering the contributions from both the inner and outer loops of a coaxial pair of circular loops, one carrying a current of 2A in one direction and the other carrying a current of 4A in the opposite direction.
Gravitational Binding Energy?
A binary system consisting of two stars, each with a mass of 2 × 10^30 kg, is in a circular orbit around their common center of mass. If the orbital speed of each star is 1.5 × 10^6 m/s, calculate the gravitational binding energy of the system. Explain why this energy is crucial for the system's stability.
Unintended Consequences?
A metal rod is rubbed against a piece of fur and then brought near a small plastic ball suspended from a thread. Suddenly, the ball starts rotating. Explain the phenomenon, citing the relevant concept from electric charges and fields.
Induction in Everyday Life?
Consider a non-contact, proximity-based public transport card. Analyze how electromagnetic induction is used in its design and operation. Explain the advantages of this technology in the given context.
Induction in a Moving Coil?
A coil is placed in a magnetic field and attached to a rotating disc that can move at varying speeds. If the rotation speed of the disc is doubled, will the induced emf in the coil also double? Explain your reasoning, considering the factors that influence the induced emf.
Rolling Sphere on a Rough Surface?
A solid sphere of radius 5 cm and mass 0.5 kg is placed on a rough surface. The sphere starts rotating with an initial angular velocity of 10 rad/s. How does the moment of inertia of the sphere affect its rotation and rolling without slipping on the rough surface?
Lenz's Law in Practice?
A coil is placed near a bar magnet. When the bar magnet is slowly moved towards the coil, a current is induced in the coil. However, if the bar magnet is moved rapidly towards the coil, the direction of induced current is reversed. Explain the difference in induced current in both scenarios.
Magnetic Domain Walls: A Quantum Conundrum?
Consider a ferromagnetic material exhibiting spontaneous magnetization. Explain how the formation of magnetic domain walls affects the material's overall magnetic moment, and discuss the implications of quantization of magnetic flux on domain wall stability.
Electric Shielding Effect?
A cylindrical shell of radius R has a charge +Q uniformly distributed on its curved surface. What is the electric field at a distance r < R from the center of the shell? Explain your reasoning with suitable diagrams and equations.
Electric Field Due to Multiple Charges?
A thin rod of length 1m is bent into a semicircle and placed on a table with its diameter along the x-axis. A point charge of +4μC is placed at the center of the semicircle and another point charge of -2μC is placed at a distance of 20cm from the center along the y-axis. Calculate the electric field at a point P, which is 30cm away from the center along the x-axis.
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