The left end of a long glass rod 7.00 cm in diameter has a convex hemispherical surface 3.50 cm in radius. the refractive index of the glass is 1.60. the glass rod is immersed in oil (n=1.45). an object placed to the left of the rod on the rod's axis is to be imaged 1.30 m inside the rod. how far from the left end of the rod must be the object be located to form the image?

Adiver in midair has an angular velocity of 6.0 rad/s and a moment of inertia of 1.2 kg·m2. he then pulls is arms and legs into a tuck position and his angular velocity increases to 12 rad/s. the net external torque acting on the diver is zero. what is his moment of inertia in the tuck position?

The ultracentrifuge is an important tool for separating and analyzing proteins. because of the enormous centripetal accelerations, the centrifuge must be carefully balanced, with each sample matched by a sample of identical mass on the opposite side. any difference in the masses of opposing samples creates a net force on the shaft of the rotor, potentially leading to a catastrophic failure of the apparatus. suppose a scientist makes a slight error in sample preparation and one sample has a mass 10 mg larger than the opposing sample. if the samples are 12 cm from the axis of the rotor and the ultracentrifuge spins at 70,000 rpm, what is the magnitude of the net force on the rotor due to the unbalanced samples? ( be thorough on your answer)

If there's a small amount of friction between two surfaces, the result could be select all that applya. no movement b. heatc. a little bit of movementd. sliding around