al phy mc 問題 b

1. The ring is a rigid body means the ring is a solid annulus.
If statement (1) is correct, all points in a rotating solid object should have the same angular velocity [w]. The linear velocity [v] is related to [w] by the equation v = r.w, where r is the distance of the point from the centre of rotation (i.e. Saturn’s centre). That is, v is proportional to r.

If statement (2) is correct, a particular satellite in the group should follow Newton’s Law of Gravitation, which provides the necessary centripetal force for the satellite to revolve round Saturn, i.e.,
GMm/r^2 = mv^2/r
where M is the mass of Saturn, m is the mass of a satellite, G is Gravitational Constant
this gives, v^2 = GM/r
v = square-root[GM/r]
or v is proportional to square-root(1/r)
You should know by now which option is the correct answer.
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2. The answer is option C
Option A is correct because potential V = kQ/R, where k is a constant, R is the radius of the concerned sphere. Since Sphere A is of radius smaller than B, V of A is thus higher than V of B
Option B is correct. Capacitance C = Q/V, the two spheres have the same charge Q, but different V. Hence, the one with smaller V(sphere B) has a larger capacitance.
Option C is wrong. Energy stored E = QV/2, for the same charge Q on the two spheres, the one with smaller V (sphere B) should possess less energy.
Option D is correct. Since sphere A has a potential higher than B, when the two spheres are connected, charges flow from high (sphere A) to low potential (sphere B). The charges on sphere A thus decrease.

http://xs.to/image-2495_4B5C3897.jpg

Consider the potential is V=kQ/r propotional to inverse of r ,

i.e. r increase -> V decrease and r decrease -> V increase ,

And rA<rB => VA>VB (stat. 1)

C=Q/V propotional to inverse V -> propotional to R

=>rA<rB => CA<CB ( stat. 2 )

cap. eneney = (1/2)CV^2 =(1/2)QV propotional to V propotional to inverse r

=>rA<rB => EA>EB ( stat. 3 wrong )



2010-01-24 22:43:05 補充：
connect together -> electron fold until no potential different

=>Va=Vb

At that them , Va decrease -> Q decrease ( V=kQ/r) ( stat.4 )

2010-01-24 22:51:01 補充：
http://xs.to/image-D1EE_4B5C3897.jpg

situation (2) , consider it is a independent object

=>G Force = cent. Force

=>GMm/r^2=mv^2/r

=>GM/r=v^2

=>v=sqrt(GM/r) = propotional to the 1/sqrt(r) B or D