Q. If a simple harmonic oscillator has a total energy E, what is the kinetic energy when the displacement is half of the amplitude?
A.E/4
B.E/2
C.3E/4
D.E
Solution
The total energy E is conserved. When the displacement is half the amplitude, the potential energy is (1/2)E, so the kinetic energy is E - (1/2)E = (1/2)E.
Q. If a solid cylinder rolls without slipping, what fraction of its total kinetic energy is translational?
A.1/3
B.1/2
C.2/3
D.1
Solution
For a solid cylinder, the total kinetic energy is KE_total = KE_translational + KE_rotational = (1/2)mv^2 + (1/2)(1/2)mR^2(ω^2). Since ω = v/R, the translational part is 2/3 of the total.
Q. If a solid cylinder rolls without slipping, what is the ratio of its translational kinetic energy to its rotational kinetic energy?
A.1:1
B.2:1
C.1:2
D.3:1
Solution
For a solid cylinder, the translational kinetic energy (KE_trans) is (1/2)mv² and the rotational kinetic energy (KE_rot) is (1/2)(Iω²). The ratio KE_trans:KE_rot is 1:2.
Q. If a solid sphere and a solid cylinder of the same mass and radius are released from rest at the same height, which will have a greater speed at the bottom?
A.Solid sphere
B.Solid cylinder
C.Both have the same speed
D.Depends on the mass
Solution
Both will have the same speed at the bottom due to conservation of energy, as they start from the same height.
Q. If a solution has a vapor pressure of 80 mmHg and the pure solvent has a vapor pressure of 100 mmHg, what is the mole fraction of the solvent?
A.0.8
B.0.75
C.0.6
D.0.5
Solution
Using Raoult's Law, the mole fraction of the solvent can be calculated as 80 mmHg / 100 mmHg = 0.8, which corresponds to a mole fraction of 0.75 for the solvent.
Q. If a stone is tied to a string and whirled in a horizontal circle of radius 2 m at a speed of 4 m/s, what is the tension in the string if the mass of the stone is 1 kg?
A.2 N
B.4 N
C.8 N
D.10 N
Solution
Centripetal force = m(v²/r) = 1(4²/2) = 8 N. Tension in the string = 8 N.
Q. If a student is selected at random from a group of 20 students, 8 of whom are girls, what is the probability that the selected student is a boy?
A.1/2
B.3/5
C.2/5
D.1/5
Solution
There are 20 - 8 = 12 boys in the group. The probability of selecting a boy is the number of boys divided by the total number of students, which is 12/20 = 3/5.
Q. If a student is selected at random from a group of 20 students, where 12 are girls and 8 are boys, what is the probability that the selected student is a boy?
A.2/5
B.1/2
C.3/5
D.1/4
Solution
The probability of selecting a boy is the number of boys divided by the total number of students, which is 8/20 = 2/5.
