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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?
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