Q. A particle moves in a straight line with a velocity v. What is its angular momentum about a point P located at a distance d from the line of motion?
A.mv
B.mvd
C.mdv
D.0
Solution
Angular momentum L = mvr, where r is the perpendicular distance from the line of motion to point P.
Q. A particle of mass m is moving in a circular path of radius r with a constant speed v. What is the angular momentum of the particle about the center of the circle?
A.mv
B.mvr
C.mr^2
D.mv^2
Solution
Angular momentum L = mvr, where v is the linear speed and r is the radius.
Q. A particle with charge q moves with velocity v in a magnetic field B. What is the expression for the magnetic force acting on the particle?
A.F = qvB
B.F = qvB sin(θ)
C.F = qB
D.F = qvB cos(θ)
Solution
The magnetic force acting on a charged particle moving in a magnetic field is given by F = qvB sin(θ), where θ is the angle between the velocity vector and the magnetic field vector.
Q. A password consists of 3 letters followed by 2 digits. How many different passwords can be formed if letters can be repeated but digits cannot? (2000)
A.17576
B.15600
C.13000
D.12000
Solution
There are 26 choices for each letter (3 letters) and 10 choices for the first digit and 9 for the second. Total = 26^3 * 10 * 9 = 17576.
Q. A pendulum of length 2 m swings from a height of 1 m. What is the speed at the lowest point of the swing? (g = 9.8 m/s²)
A.4.4 m/s
B.3.1 m/s
C.2.8 m/s
D.5.0 m/s
Solution
Using conservation of energy, potential energy at the top = kinetic energy at the bottom. mgh = 0.5mv². Solving gives v = sqrt(2gh) = sqrt(2 * 9.8 * 1) = 4.4 m/s.
Q. A pendulum swings from a height of 2 m. What is the speed at the lowest point of the swing?
A.2 m/s
B.4 m/s
C.6 m/s
D.8 m/s
Solution
Using conservation of energy, potential energy at the top = kinetic energy at the bottom. mgh = 0.5mv². Solving gives v = √(2gh) = √(2 * 9.8 * 2) = 4 m/s.
Q. A pendulum swings from a height of 5 m. What is the speed at the lowest point of the swing?
A.5 m/s
B.10 m/s
C.15 m/s
D.20 m/s
Solution
Using conservation of energy, potential energy at the top = kinetic energy at the bottom. mgh = 0.5mv^2. Solving gives v = sqrt(2gh) = sqrt(2*9.8*5) = 10 m/s.
Q. A pendulum swings with a period of 1 second. If the length of the pendulum is increased to four times its original length, what will be the new period?
A.1 s
B.2 s
C.4 s
D.√4 s
Solution
The period of a pendulum is given by T = 2π√(L/g). If L is increased to 4L, T becomes 2π√(4L/g) = 2T = 2 seconds.