AP Physics C Mechanics - 5.3 Torque- Exam Style questions- MCQs
Torque AP Physics C Mechanics MCQ
Unit 5: Torque and Rotational Dynamics
Weightage : 10-15%
Unit 5: Torque and Rotational Dynamics
Weightage : 10-15%
A mass hangs from two ropes at unequal angles, as shown above. Which of the following makes correct comparisons of the horizontal and vertical components of the tension in each rope?
| Option | Horizontal Tension | Vertical Tension |
|---|---|---|
| (A) | Greater in rope B | Greater in rope B |
| (B) | Equal in both ropes | Greater in rope A |
| (C) | Greater in rope A | Greater in rope A |
| (D) | Equal in both ropes | Equal in both ropes |
| (E) | Greater in rope B | Equal in both ropes |
Answer: (B)
Solution:
Since the mass is in static equilibrium, the net force in both the horizontal and vertical directions is zero.
In the horizontal direction, the only forces are the horizontal components of the two tensions. Therefore,
\(T_A\cos\theta_A=T_B\cos\theta_B\).
Thus, the horizontal components of the tensions are equal.
In the vertical direction, the vertical components must support the weight of the mass:
\(T_A\sin\theta_A+T_B\sin\theta_B=mg\).
Rope A makes the larger angle with the horizontal, so a greater fraction of its tension acts vertically. Hence, the vertical component of the tension is greater in rope A.
Therefore, the correct comparison is:
Which of the following conditions are necessary for an object to be in static equilibrium?
I. The vector sum of all torques on the object must equal zero.
II. The vector sum of all forces on the object must equal zero.
III. The sum of the object’s potential and kinetic energies must be zero.
(A) I only
(B) II only
(C) III only
(D) I and II only
(E) I, II, and III
Answer: (D) I and II only
Solution:
For an object to be in static equilibrium, it must remain at rest without translating or rotating.
Therefore, the following conditions must both be satisfied:
\(\sum \vec{F}=0\)
\(\sum \tau=0\)
Condition I is necessary because a nonzero net torque would cause rotational acceleration.
Condition II is necessary because a nonzero net force would cause linear acceleration.
Condition III is not necessary. In static equilibrium, the kinetic energy is zero, but the potential energy can have any value depending on the chosen reference level. For example, an object suspended above the ground has gravitational potential energy while remaining in static equilibrium.
Hence, only statements I and II are required.
Which of the following ranks the torques applied by the three equal forces \(A\), \(B\), and \(C\) to the long thin rod about its fixed axis as indicated?
Correct Answer: \(\boxed{\mathrm{D}}\)
The magnitude of torque is given by
\(\tau=rF\sin\theta\)
where \(r\) is the perpendicular distance from the axis of rotation to the line of action of the force.
Force \(C\) acts along the length of the rod, so its line of action passes through the axis of rotation. Thus, \(\theta=180^\circ\) (or equivalently, the perpendicular lever arm is zero), giving
\(\tau_C=0\)
Forces \(A\) and \(B\) are both perpendicular to the rod, so \(\sin90^\circ=1\). Their torques depend only on their lever arms.
Force \(B\) is applied farther from the axis of rotation than force \(A\), so
\(\tau_B>\tau_A\)
Therefore, the torques are ranked as
\(\tau_B>\tau_A>\tau_C\)
Hence, the correct answer is (D).