Every Question
Answered.
Board exam questions from CBSE, ICSE, and all State Boards — answered with AI-structured explanations and community insights.
A Bungee Jumper's Surprise
Rahul, a bungee jumper, jumps from a 200 m high bridge. His bungee cord is designed to stretch by 50 m before releasing the stored elastic potential energy. Calculate the speed with which Rahul hits the water on the ground, given that the centre of mass of his body comes to rest momentarily at 20 m above the ground.
Mass and Gravitational Force?
Suppose a planet with a mass twice that of the Earth is discovered. If a body of mass 100 kg is placed on its surface, how will the gravitational force acting on it compare to the force acting on the same body on the Earth's surface?
Tipping Point of Gyroscope?
A gyroscope is mounted on a frictionless rotating turntable. If the gyroscope's angular velocity is 2 rad/s about its axis of symmetry, and it experiences a torque of 0.5 Nm perpendicular to its axis, determine the minimum angular velocity the turntable must have to prevent the gyroscope from tipping.
A Car's Braking System - Efficiency and Safety?
A car is moving at a speed of 50 m/s when the driver suddenly applies the brakes. The car's mass is 1500 kg. If the brakes are applied uniformly over a distance of 20 m, will the car come to a complete stop? If not, what would be the remaining speed of the car and how does it relate to the coefficient of kinetic friction between the car's tires and the road?
Angular Momentum Conservation in Rotational Motion?
In a laboratory experiment, a top spinning on a string is released from rest when the string's length is halved. Analyze how the angular momentum of the top changes and relate it to the conservation of angular momentum principle.
Relative Velocity Puzzle?
A car A is moving with a uniform velocity of 20 m/s due east. A car B is moving with a uniform velocity of 15 m/s due north. If a bird flying at a velocity of 30 m/s in a direction making an angle of 60° with the horizontal meets car A, explain the relative velocity of the bird with respect to car B.
A Rotating Wheel's Inertia?
A bicycle wheel has a mass of 8 kg and a radius of 0.5 m. It is initially at rest. If a wheel has 50% of its kinetic energy at rotation, calculate the linear velocity of the bicycle's center of mass when the wheel is rotating with an angular velocity of 10 rad/s.
Inclined Plane and Friction?
A block of wood of mass 5 kg is placed on an inclined plane of angle 30°, where the coefficient of kinetic friction is 0.2. If a force of 25 N is applied parallel to the plane, explain the situation with a neat diagram and describe the net force acting on the block in terms of its components.
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.
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.
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.
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.
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.
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?
Gravitational Field Strength at a Distance?
A 5 kg object is placed at the center of a planet with a mass of 8 x 10^24 kg. If the gravitational field strength at a distance of 2 R from the center of the planet is 3 N/kg, what would be the gravitational field strength at a distance of 4 R from the center of the planet, where R is the radius of the planet?
A Spring in Action?
A 2 kg block attached to a horizontal spring is oscillating with a frequency of 2 Hz. If the block is given an upward impulse of 5 Ns, how will it affect the subsequent oscillations?
A Bungee Jumper's Kinetic Energy
A bungee jumper of mass 60 kg jumps from a height of 50 m. Assuming 80% of the potential energy is converted into kinetic energy just before the jumper hits the ground, calculate the speed of the jumper.
Gravitational Redshift in Motion
A spacecraft travels close to a massive object and emits a photon. The photon is observed to have shifted in frequency due to gravitational redshift. How would the photon's frequency change if the spacecraft were moving at high speed relative to the observer?
Torque on a Couple of Pulleys?
Ashish is using a system of two pulleys to lift a load of 100 N. The first pulley is connected to a fixed point and the second pulley is connected to a horizontal beam, which exerts a force of 20 N on the first pulley. If the radius of the pulleys is 5 cm, what is the angular acceleration of the load when it is lifted at a constant rate of 1 m/s^2?
Have an academic question?
Stuck on a concept? Ask here — whether it's CBSE, ICSE, competitive exams, or any other subject you're learning. Our community and AI engine will answer with structured, exam-ready explanations.