Though most tennis players generally strive to strike the ball on the

Question

Though most tennis players generally strive to strike the ball on the racket’s vibration node, more commonly known as the “sweet spot,” many players are unaware of the existence of a second, lesser-known location on the racket face, the center of percussion, that will also greatly diminish the strain on a player’s arm when the ball is struck.

In order to understand the physics of this second sweet spot, it is helpful to consider what would happen to a tennis racket in the moments after impact with the ball if the player’s hand were to vanish at the moment of impact. The impact of the ball would cause the racket to bounce backward, experiencing a translational motion away from the ball. The tendency of this motion would be to jerk all parts of the racket, including the end of its handle, backward, or away from the ball. Unless the ball happened to hit the racket precisely at the racket’s center of mass, the racket would additionally experience a rotational motion around its center of mass—much as  a penny that has been struck near its edge  will start to spin. Whenever the ball hits the racket face, the effect of this rotational motion will be to jerk the end of the handle forward, toward the ball. Depending on where the ball strikes the racket face, one or the other of these motions will predominate.

However, there is one point of impact, known as the center of percussion, which causes neither motion to predominate; if a ball were to strike this point, the impact would not impart any motion to the end of the handle. The reason for this lack of motion is that the force on the upper part of the hand would be equal and opposite to the force on the lower part of the hand, resulting in no net force on the tennis player’s hand or forearm. The center of percussion constitutes a second sweet spot because a tennis player’s wrist typically is placed next to the end of the racket’s handle. When the player strikes the ball at the center of percussion, her wrist is jerked neither forward nor backward, and she experiences a relatively smooth, comfortable tennis stroke. The manner in which a tennis player can detect the center of percussion on a given tennis racket follows from the nature of this second sweet spot. The center of percussion can be located via simple trial and error by holding the end of a tennis racket between your finger and thumb and throwing a ball onto the strings. If the handle jumps out of your hand, then the ball has missed the center of percussion.    1 
 1. What is the primary message the author is trying to convey?

(A) A proposal for an improvement to the design of tennis rackets
 (B) An examination of the differences between the two types of sweet spots
 (C) A definition of the translational and rotational forces acting on a tennis racket
(D) A description of the ideal area in which to strike every ball
(E) An explanation of a lesser-known area on a tennis racket that dampens unwanted vibration

2  
 2. According to the passage, all of the following are true of the forces acting upon a tennis racket striking a ball EXCEPT

(A) the only way to eliminate the jolt that accompanies most strokes is to hit the ball on the center of percussion
 (B) the impact of the ball striking the racket can strain a tennis player’s arm
(C) there are at least two different forces acting upon the racket the end of the handle of the racket will jerk forward after
 (D) striking the ball unless the ball strikes the racket’s center of mass
(E) the racket will rebound after it strikes the ball

3  
  3. What is the primary function served by paragraph 2 in the context of the entire passage?

(A) To establish the main idea of the passage 
(B) To provide an explanation of the mechanics of the phenomenon discussed in the passage
 (C) To introduce a counterargument that elucidates the main idea of the passage
 (D) To provide an example of the primary subject described in the passage
 (E) To explain why the main idea of the passage would be useful for tennis players

4  
 4. The author mentions “a penny that has been struck near its edge” ( Highighted ) in order to

(A) show how the center of mass causes the racket to spin
(B) argue that a penny spins in the exact way that a tennis racket spins
(C) explain how translational motion works
(D) provide an illustration of a concept
 (E) demonstrate that pennies and tennis rackets do not spin in the same way

5  
 5. Which of the following can be inferred from the passage?

(A) If a player holds the tennis racket anywhere other than the end of the handle, the player will experience a jolting sensation.
 (B) The primary sweet spot is more effective at damping vibration than is the secondary sweet spot.
 (C) Striking a tennis ball at a spot other than the center of percussion can result in a jarring feeling.
 (D) Striking a tennis ball repeatedly at spots other than a sweet spot leads to “tennis elbow.”
(E) If a player lets go of the racket at the moment of impact, the simultaneous forward and backward impetus causes the racket to drop straight to the ground.

6

“The reason for this lack of motion is that the force on the upper part of the hand would be equal and opposite to the force on the lower part of the hand, resulting in no net force on the tennis player’s hand or forearm.” 
 
  6. Select the sentence in the second or third paragraph that describes the physics of the center of percussion’s perceived sweetness.

7  
 7. It can be inferred that a tennis ball that strikes a racket’s center of percussion will do which of the following?

Indicate all that apply.

A. Cause the racket to bounce backward
B. Not cause the wrist to jerk
C. Allow for a cleaner stroke than a ball striking a racket’s primary sweet spot

Sajjad1994 · Answer

OE

1. What is the primary message the author is trying to convey?

The first paragraph introduces the idea that there are two sweet spots on the face of a tennis racket: one well-known spot and another  “lesserknown”  spot. The second and third paragraphs detail how the mechanism of the second sweet spot, the center of percussion, works. The fourth paragraph describes a way to find the center of percussion. 
 
 A)  Nothing in the passage suggests that the author is trying to propose an improvement to the design of tennis rackets.

B)  The passage does mention both types of sweet spots in the first paragraph, but it does not focus on the differences between the two.

C)  Paragraph 2 explains the types of forces acting on the racket, but this topic is too narrow to be the primary message of the overall passage. The passage as a whole focuses on the idea of sweet spots in general.

D)  While the passage does mention one benefit of hitting the ball on a sweet spot, it does not claim that this is the  “ideal area”  to hit  “every”  ball. There may be other areas that convey other benefits. The word every is too extreme. 
 
  E) CORRECT.   The passage introduces the notion of a  “second, lesser-known”  sweet spot and explains how it works.

Answer: E

Sajjad1994 · Answer

OE

2. According to the passage, all of the following are true of the forces acting upon a tennis racket striking a ball EXCEPT

EXCEPT questions require you to validate the answer choices. Go through the choices one by one, labeling true answers with a T and the one false answer with an F.

A) CORRECT.    False. This choice contradicts information given in the first paragraph: the center of percussion is only one of two   sweet spots that minimize vibration. The vibration node is the   other sweet spot.

B)     True.  The first paragraph introduces the concept that the impact can  “strain”  the player’s arm.

C) True.  The second paragraph describes at least two different forces that act upon a tennis racket striking the ball:    “translational,”  as described in the second and third sentences,   and  “rotational,”  as described in the fourth and fifth sentences.

D) True.  The fourth sentence of the second paragraph states that    “unless the ball happened to hit the racket precisely at the racket’s   center of mass, the racket would additionally experience a     rotational motion.”  The fifth sentence then reads:  “Whenever the     ball hits the racket face, the effect of this rotational motion will   be to jerk the end of the handle forward, toward the ball.”  
 
 E) True.  The second sentence of the second paragraph states that a racket will  “bounce backward”  after striking the ball; these words are synonyms for rebound. 
  
  Answer: A

Sajjad1994 · Answer

OE

3. What is the primary function served by paragraph 2 in the context of the entire passage?

Paragraph 2 introduces and explains, in great detail, the forces that act on a racket when striking a ball. 
 
 A)  The main idea is established in the first paragraph: there is a second sweet spot that results in minimal vibration when a tennis racket strikes a ball.

B) CORRECT.   This matches the function of the second paragraph, which explains the forces that occur when a racket strikes a ball.

C)  The second paragraph introduces the forces that act on a racket when striking a ball. This follows from the main idea; it is not a counterargument.

D)  While the second paragraph does provide an example, this is not an example of the center of percussion, which is the primary subject described in the passage. The example helps to explain the forces behind the center of percussion, but is not itself an example of a center of percussion.

E)  The first and third paragraphs, not the second paragraph, make reference to why tennis players would want to know about the sweet spot: to minimize strain on the arm. 
 
  Answer: B

Sajjad1994 · Answer

OE

4. The author mentions “a penny that has been struck near its edge” (     Highighted     ) in order to

The passage says that  “the racket would additionally experience a rotational motion around its center of mass—much as a penny that has been struck near its edge will start to spin.”  In other words, the motion of the penny is an example that closely mimics the situation with the tennis racket. The correct answer should match this characterization.

A)    The center of mass does not cause the racket to spin; rather, a ball striking the racket causes it to spin.

B)    The author does not present the information about the penny as an argument; rather, it is an example. In addition, the author implies, via the words    “much as,”    that the penny and the racket spin in similar ways; this is not the same as saying that they spin in the    “exact”    same way.

C)    This sentence is about rotational motion, not translational motion.

D) CORRECT.    The example of the penny is an analogy for the rotational motion experienced by the tennis racket.

E)  The example is intended to demonstrate a situation in which tennis rackets and pennies do spin in similar ways.

Answer: D

Sajjad1994 · Answer

OE

5. Which of the following can be inferred from the passage?

Because the question applies to the whole passage, examine the answer choices first. It is useful to remember that when the GRE asks you to infer, you need to base the inference only on information presented in the passage.

A)    The passage does explain that holding the racket at the end of the handle and hitting the ball at a particular spot results in a comfortable stroke that reduces the strain on a player’s arm. It does not address, however, what would happen if the player grasped the racket at a different point. It is possible that grasping the racket at another point would simply result in a different center of percussion.

B)    The passage states that there is one commonly known sweet spot and a second, lesser-known sweet spot. However, the passage says nothing about the relative efficacy of these two sweet spots.

C) CORRECT.    You are told that playing tennis can result in strain on a player’s arm. You are also told that striking the ball at the center of percussion leads to a “smooth, comfortable stroke,” or one which does not cause the same kind of damage as a regular stroke. Striking the ball at a spot other than the center of percussion, then, could lead to a jarring stroke, or one that could cause damage to a player’s arm. 
 
  D)  The passage mentions nothing about  “tennis elbow”  or what behavior can result in this injury; it merely talks about  “strain.”  Be careful not to add additional information beyond what is presented in the passage.

E)  The second paragraph obliquely addresses a situation in which a tennis player lets go of the racket at the moment of impact. However, this question does not specify the point at which the tennis ball struck the racket. If the ball did not strike a sweet spot, the racket may have some translational or rotational force transferred from the ball and so might not drop straight to the ground. 
  
  Answer: C

Sajjad1994 · Answer

OE

6. Select the sentence in the second or third paragraph that describes the physics of the center of percussion’s perceived sweetness.

This is a very specific Select-in-Passage question, asking you to find something in the highly complex second and third paragraphs. The second paragraph of the passage explores what happens when a ball strikes a racket in general, but doesn’t go into any detail about the sweet spot itself. The sentence you want will be in the third paragraph.

The correct sentence is the second sentence of the third paragraph:  “The reason for this lack of motion is that the force on the upper part of the hand would be equal and opposite to the force on the lower part of the hand, resulting in no net force on the tennis player’s hand or forearm.”  The final sentence of this paragraph describes the effects of hitting this second sweet spot, but it does not describe the actual physics of the sweetness.

Sajjad1994 · Answer

OE

7. It can be inferred that a tennis ball that strikes a racket’s center of percussion will do which of the following?

This is a Select-One-or-More question. The answers are likely to be found in the first or third paragraphs, as the second explores a hypothetical situation and the fourth describes how to find the center of percussion.

A.  The passage states that the ball would cause the racket to bounce backward in a hypothetical situation: if the player’s hand were to vanish at the moment of impact. This part of the passage is not discussing what happens with a real stroke at the center of percussion.

B. CORRECT.    The last sentence of the third paragraph says that a player who strikes the center of percussion will not have his or her wrist jerked  “forward or backward.”

C.  The passage does state that when someone hits the center of percussion, the player will experience  “a relatively smooth, comfortable tennis stroke.”  The passage never compares this situation, however, to what happens when the player hits the primary sweet spot. The passage doesn’t indicate whether one is cleaner than the other or whether they’re both the same.

Answer: B

Though most tennis players generally strive to strike the ball on the

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