Question
29 to 32
Consider four objects, each having the same mass and the same radius: 1. a solid sphere 2. a hollow sphere 3. a flat disk in the x, y plane 4. a hoop in the x, y plane The order of increasing rotational inertia about an axis through the center of mass and parallel to the z axis is: A) 1, 2, 3, 4 B) 4, 3, 2, 1 C) 1, 3, 2, 4 D) 4, 2, 3, 1 E) 3, 1, 2, 4 For a block of mass w to slide without friction up the rise of height in shown it must have a minimum initial kinetic energy of A) gh B) 2wgh C) gh2 D) wgh E) wgh2 A projectile is fired straight upward from Earth's surface with a speed that is half the escape speed. If it is the radius of Earth, the highest altitude reached, measured from the surface, is: A) R/4 B) R/3 C) R/2 D) R E) 2R The ideal mechanical advantage (i.e. the ratio of the weight W to the pull P for equilibrium) of the combination of ideal pulleys shown below is:
Explanation / Answer
29.
Isolidsphere = 2 m r^2 / 5 = 0.4 m r^2
Ihollowphere = 2 mr^2/3 = 0.667 m r^2
Idisc = m r^2 /2 = 0.5 m r^2
Ihoop = m r^2
1 < 3 < 2 < 4
Ans(C)
30. KE = m g h
Ans(D)
31. escape KE = G M m / Re
so initial KE = G M m / 4Re { Ke = m v^2 /2 }
using energy conservation,
G M m / 4Re - G M m / Re = 0 - G M m / (Re + h)
0.25/Re - 1/Re = - 1 / (Re + h)
Re + h = Re / 0.75
h = R/3
Ans(B)
32. 2T = w
T = 2p
4p = w
w/p = 4
ans(D)