3 . A block of mass (m) and a sphere of mass (m) with a radius of R are propelled up inclines of the
same shape with identical velocities (v ). The block moves up a frictionless incline, while the
sphere’s incline has enough friction so that the sphere rolls without slipping. The initial velocity is
large enough that both fly off the upper end of the inclines and land some distance away to the right, as
shown in the figure. Which of the following statements is correct?
(A) The block will land farther to the right because the friction acting on the sphere does negative
work, causing the sphere to lose mechanical energy.
(B) The block and sphere land the same distance to the right because after leaving the incline, both
accelerate downward at the same 9.8 m/s^2 .
(C) The block and sphere land the same distance to the right because the horizontal velocity of both
remains constant after leaving the incline.
(D) The block and sphere land the same distance to the right because both gain the same gravitational
potential energy moving up the incline.
(E) The sphere will travel farther because it loses less translational kinetic energy moving up the
incline than the block.
4 . A compound pulley consists of two discs of radius (R ) and (2R ) that are connected and rotate freely
about a horizontal axle. The total rotational inertia of the pulley is I . Two masses are connected to the
pulley by light strings, as shown in the figure. When the masses are released, the angular acceleration
of the pulley will be
(A)