Electromagnetism - Electric Force

Two identical conducting spheres, A and B, carry equal charge. They are initially separated by a distance much larger than their diameters, and the force between them is F. A third identical conducting sphere, C, is uncharged. Sphere C is first touched to A, then to B, and then removed. As a result, the force between A and B is equal to.

A. 0
B. F/16
C. F/4
D. 3F/8
E. F/2

(GR9677 #24)

Solution:

Coulomb's Law, F_i = kq_Aq_B/r² 
q_A = q_B = Q
F_i = F = kQ² /r² 

When uncharged sphere C touches A, charge A distributes itself evenly:
q_C = q_A' = ¹/₂ q_A = ¹/₂Q

When sphere C touches B:
q_C'  = q_B'  = ¹/₂(q_C + q_B) = ¹/₂(¹/₂Q + Q) = ³/₄Q

Therefore,
F_f  = kq_A' q_B'/r² 
= k (¹/₂Q) (³/₄Q)/r²
= ³/₈ kQ²/r² 
= ³/₈ F

Answer: D

Nuclear & Particle Physics - Bonding Mechanism

Solid Argon is held together by which of the following bonding mechanism?

A. Ionic bond only
B. Covalent bond only
C. Partly covalent and partly ionic bond
D. Metallic bond
E. Van der Waals bond

(GR9277 #24)

Solution:

Solid argon →  a noble gas full outermost electron shell

(A) FALSE
Ionic bond only → giving/receiving electron

(B) FALSE
Covalent bond only → sharing electron

(C) FALSE
Partly covalent and partly ionic bond

(D) FALSE
Metallic bond → a positive charge/nucleus swimming in a sea of free electron → FALSE

(E) TRUE
Van der Waals bond:

• occur between atoms or molecules of the same type
• occur due to variances in charge distribution in the atom

Answer: E 

Electromagnetism - Electric Circuit

The battery in the diagram above is to be charged by the generator G. The generator has a terminal voltage of 120 volts when the charging current is 10 Amperes. The battery has an emf of 100 volts and an internal resistance of 1 Ohm. In order to charging current, the resistance R should be set at 

A. 0.1 Ω
B. 0.5 Ω
C. 1.0 Ω
D. 5.0 Ω
E. 10.0 Ω

(GR8677 # 24)

Solution:

Potential difference across the resistor R:

V = IR_t = V_Generator − V_Battery = 120 − 100 = 20 V

Total resistance:

R_t = R + R_internal = R + 1

V = IR_t = I(R + 1) = 10(R + 1) = 20 V
R = 1 Ω

Answer: C

Classical Mechanics - Kinematics

A stone is thrown at an angle 45^o above the horizontal x-axis in the +x-direction. If air resistance is ignored, which of the velocity versus time graphs shown above best represent v_x versus t and v_y versus t, respectively?

	vx versus t	vy versus t
A.	I	IV
B.	II	I
C.	II	III
D.	II	V
E.	IV	V

(GR0177 #24)

Solution:

An object such as a cannonball is fired at an angle to the ground:

• The shape of the path or its trajectory is parabolic
• In the x-direction, the object travels at constant speed
• In y-direction, we treat the object as if it were tossed directly upward (positive velocity) and then returned to the ground (negative velocity → the object reverses the direction of its motion).

Answer: C