29 to 32 Consider four objects, each having the same mass and the same radius: 1

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)

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