1. Apply the equation: s = ut + (1/2)at^2 to the vertical motion from R to S
with s = -10m, u = 0 m/s, a = -g(=-9.81 m/s^2), t =?
hence, -10 = (1/2).(-9.81)t^2
t = 1.428 s
Hence, horizontal speed of monkey = 7/1.428 m/s = 4.9 m/s
The answer is option B
2. Let b be the angular position of the 4th order maximium, and c be the angular position of the 2nd order maximium.
Hence, a.sin(c) = 2入
and a.sin(b) = 4入
where a is the grating slit separation and 入 is the wavelength of light used.
Dividing, sin(c)/sin(b) = 2入/ 4入 = 1/2
i.e. sin(c) = sin(b)/2
The max vlaue of sin(b) = 1, hence, sin(c) < 1/2
i.e. c < 30 degrees
The answer is thus option B (i.e. choose the nearest angle below 30 degrees)
[ Option A is wrong because when the 2nd order max is at 15 degrees, the max order of fringe is 7, not 4]
3. Suppose the electron is at distance d from the -ve plate
Change in potential of electron = (Vo).(d/D)
where Vo is the voltage between the two plates, with separation D.
Hence, drop in potential energy of electron = e.(Vo)(d/D)
where e is the electronic charge
By conservation of energy,
(KEo) + e(Vo)(d/D) = KE
where (KEo) is the initial kinetic energy, and KE is the kinetic energy at distance d.
Thus, KE = [e(Vo)/D].d + (KEo)
The graph of KE against d is a straight line with +ve slope of value [e(Vo)/D].
The answer is option A
4. The answer is option C.
Statement 1 is wrong because the straight line of M doesn't pass through the origin. Hence, V and I are NOT proportional.
5. When S is closed,
99 = 100R/(100+R)
R = 9900 ohms
When S is open, the 100-ohm is in parallel with 2R
Equivalent resistance = 100 x 2R/(100+2R) = 99.5 ohms
The answer is option C
(Since the "word limit" is reached, I give answer to Q6 and 7 in the opinion (意見) section.)
2013-03-09 17:50:32 補充：
6. Magnetic force at X due to Y and Z, Fx = [-k(2).(1)/(2) + k(2).(3)/4] = 0.5k
where k is a constant
Magnetic force at Y due to X and Z, Fy = [k.(1).(2)/2 k(1).(3)/2] N = 2.5k
Magnetic force at Z due to X and Y, Fz = [k(2).(3)/4 + k(1).(3)/2] = 3k
2013-03-09 17:51:09 補充：
6(cont'd) Hence, the greatest magnetic force is experienced by Z, and the least force by X.
The answer is option C.
2013-03-09 17:51:36 補充：
7. There are 3 forces acting on the kite, the kite weight of 0.2g, the string tension 15 N and the wind force F. The 3 forces are in equilibrium, and hence forms a triangle (Principle of Triangle of Forces). The angle bewteen the kite weight and the string tension is (90+35) degrees = 125 degrees.
2013-03-09 17:52:03 補充：
7(cont'd) By the cosine rule,
F^2 = [(0.2g)^2 + 15^2 - 2 x 0.2g x 15.cos(125) ] N^2
where g is the acceleration due to gravity
F = 16.2 N
The answer is option B