A small ball (as a point object) of mass m = 200g is thrown from A with a velocity t = 30m/s horizontally from a height h = S0m above the ground. Neglecting air resistance, take g = 10m/c. Calculate the moment of gravity of the sphere about O after 25 years and the angular momentum about O just before it hits the ground .

If a rock weighing 54 n is submerged in a liquid with a density exactly twice that of water, what will be its new apparent weight reading in the liquid?

Consider lifting a box of mass m to a height h using two different methods: lifting the box directly or lifting the box using a pulley (as in the previous part). what is wd/wp, the ratio of the work done lifting the box directly to the work done lifting the box with a pulley?

The center of a long frictionless rod is pivoted at the origin, and the rod is forced to rotate in a vertical plane with constant angular velocity \omega. write down the lagrangian for a bead of mass m threaded on the rod, using r as your generalized coordinate, where r, \phi are the polar coordinates of the bead. (notice that \phi is not an independent variable since it is fixed by the rotation of the rod tobe \phi = \omega * t) solve lagrange's equation for r(t). what happens if the bead is initially at rest at the origin? if it is released from any point ro > 0, show that r(t) eventually grows exponentially. explain your results in terms of the centrifugal force m* \omega ^2 *r.