Q. A wave traveling along a string is described by the equation y(x, t) = A sin(kx - ωt). If A = 2 m, k = 3 rad/m, and ω = 6 rad/s, what is the amplitude of the wave?
A.1 m
B.2 m
C.3 m
D.4 m
Solution
The amplitude of the wave is given directly by A in the wave equation. Here, A = 2 m.
Q. A wave traveling along a string is described by the equation y(x, t) = A sin(kx - ωt). What does the parameter A represent?
A.Wavelength
B.Amplitude
C.Frequency
D.Speed
Solution
In the wave equation y(x, t) = A sin(kx - ωt), A represents the amplitude of the wave, which is the maximum displacement from the equilibrium position.
Q. A wheel is rotating with an angular velocity of 10 rad/s. If it accelerates at a rate of 2 rad/s², what will be its angular velocity after 5 seconds?
Q. A wheel of radius R is rolling without slipping on a horizontal surface. What is the relationship between the linear velocity v of the center of the wheel and its angular velocity ω?
A.v = Rω
B.v = ω/R
C.v = 2Rω
D.v = ω/2R
Solution
For rolling without slipping, the linear velocity v is related to angular velocity ω by the equation v = Rω.
Q. A wheel of radius R rolls on a flat surface. If it rolls without slipping, what is the distance traveled by the center of mass after one complete rotation?
A.2πR
B.πR
C.4πR
D.R
Solution
The distance traveled by the center of mass after one complete rotation is equal to the circumference of the wheel, which is 2πR.
Q. A wheel of radius R rolls without slipping on a horizontal surface. If it rotates with an angular velocity ω, what is the linear velocity of the center of the wheel?
A.Rω
B.2Rω
C.ω/R
D.R/ω
Solution
The linear velocity v of the center of the wheel is related to the angular velocity ω by the equation v = Rω.
Q. A wheel of radius R rolls without slipping on a horizontal surface. If the wheel has an angular velocity ω, what is the linear velocity of the center of the wheel?
A.Rω
B.ω/R
C.ω
D.R/ω
Solution
The linear velocity v of the center of the wheel is related to the angular velocity by v = Rω.
Q. A wire has a resistance of 12 Ω and is made of a material with a resistivity of 3 x 10^-6 Ω·m. If the length of the wire is 4 m, what is its cross-sectional area?
Q. A wire made of material A has a resistivity of 1.5 x 10^-8 Ω·m, while material B has a resistivity of 3.0 x 10^-8 Ω·m. If both wires have the same dimensions, which wire will have a higher resistance?
A.Wire A
B.Wire B
C.Both have the same resistance
D.Cannot be determined
Solution
Resistance is directly proportional to resistivity; hence, wire B with higher resistivity will have higher resistance.
Q. A wire made of material A has twice the length and half the cross-sectional area of a wire made of material B. If the resistivity of A is ρ, what is the resistance of wire A in terms of the resistance of wire B?
A.2R
B.4R
C.R/2
D.R/4
Solution
Resistance R = ρ(L/A). For wire A, R_A = ρ(2L/(A/2)) = 4ρ(L/A) = 4R_B.
Q. A wire of length L and cross-sectional area A is stretched by a force F. If the Young's modulus of the material is Y, what is the extension of the wire?
A.F * L / (A * Y)
B.A * Y * L / F
C.F * A / (Y * L)
D.Y * L / (F * A)
Solution
The extension of the wire can be calculated using the formula: extension = (F * L) / (A * Y).
