Two balls are dropped from heights h and 2h respectively. What would be the ratio of times taken by the balls to reach the earth?a)andradic;2 1b)1 andradic;2c)2 1d)4 119Correct answer is option 'B'. Can you explain this answer?

Explore Courses UPSC Exam UPSC Test Series Free Notes EduRev Infinity

Open App

ACT Exam > ACT Questions > Two balls are dropped from heights h and 2h r...

Two balls are dropped from heights h and 2h respectively. What would be the ratio of times taken by the balls to reach the earth?

a)
√2 ∶ 1
b)
1 ∶ √2
c)
2 ∶ 1
d)
4 ∶ 119

Correct answer is option 'B'. Can you explain this answer?

Join for Free

Join for Free

Verified Answer

Two balls are dropped from heights h and 2h respectively. What would b...

Concept:

For a body moving in a straight line with constant acceleration, then

v = u + at --- (1)
s = ut + 0.5at² --- (2)
v² = u² + 2as --- (3)
Where u = initial velocity, v = final velocity, a = acceleration, s = displacement, t = time

Calculation:

Given that, for first ball, height, h₁ = h and let time = t₁

And for the second ball, height, h₂ = 2h and time = t₂

Since the object is falling freely then acceleration = g

Initial velocity for both the bodies, u = 0

Then from equation 2, for first ball

h₁ = ut + 0.5gt₁²

⇒ h = 0 + 0.5gt₁²--- (4)

For second ball,

h₂ = ut + 0.5gt₂²

⇒ 2h = 0 + 0.5gt₂² --- (5)

Dividing equation 4 by 5

View all questions of this test

Most Upvoted Answer

Two balls are dropped from heights h and 2h respectively. What would b...

Ratio of times taken by the balls to reach the earth:
- Let's assume the height from which the balls are dropped is h for the first ball and 2h for the second ball.
- The time taken by an object to fall from a certain height can be calculated using the formula: time = √(2h/g), where g is the acceleration due to gravity (approximately 9.8 m/s²).

Time taken by the first ball (h):
- For the first ball dropped from height h, the time taken to reach the earth can be calculated as: t1 = √(2h/g).

Time taken by the second ball (2h):
- For the second ball dropped from height 2h, the time taken to reach the earth can be calculated as: t2 = √(2(2h)/g) = √(4h/g) = 2√(h/g).

Ratio of times taken by the two balls:
- To find the ratio of times taken by the two balls, we divide the time taken by the second ball by the time taken by the first ball: t2/t1 = 2√(h/g) / √(2h/g) = 2√(h/g) / √(2h/g) = 2√(h/g) * √(g/2h) = 2√(h/2h) = 2√(1/2) = √2.
Therefore, the ratio of times taken by the two balls to reach the earth is √2, which corresponds to option b) 1 √2.

Answered by Orion Classes · View profile

View all answers Start learning for free

Explore Courses for ACT exam

Similar ACT Doubts

Directions:In the passages that follow, some words and phrases are underlined and numbered. In the answer column, you will ﬁnd alternatives for the words and phrases that are underlined. If you think that the original version is best, choose “NO CHANGE,”. You will also ﬁnd questions about a particular section of the passage, or about the entire passage. These questions will be identiﬁed either by an underlined portion or by a number in a box. Look for the answer that clearly expresses the idea, is consistent with the style and tone of the passage, and makes the correct use of standard written English. Read the passage through once before answering the questions. For some questions, you should read beyond the indicated portion before you answer.PassageBody ArmorIf you were an officer of the law or an armed military person, would you prefer to wear a “bullet-proof vest” or “soft body armor” under your (1) suit and uniform?(2) Most often the person would probably opt for the bullet-proof vest, as its name tends to denote a higher level of security. The problem, though, is that no“bullet-proof vest” (3) is really bullet-proof. In fact, there is no protective clothing currently available that offers complete protection from firearms.As weaponry and ammunition have changed through (4) the centuries; so have the materials from which protective clothing is made. During the black powder era of the 1700s, silk (5) was the material of choice to ward off injury or death from a black powder ball. Black powder propelled lead balls were much slower than present-day bullets, and silk was sometimes fairly effective protection against weapons at longer ranges. During World War II, the “flak jacket” was developed as a protective device. (6) Soon, the best this attire could do was to protect the wearer from shrapnel, not from the bullets themselves. (7) Today’s modernprotective vests are made from a variety of synthetic materials, some of which are (8) more with effectiveness than others. The idea is to produce a material that is strong enough to ward off high-speed bullets yet light enough to allow for ease of movement. This can be a daunting task when cost is also considered,(9)Most people have the idea that protective gear causes a bullet to deflect off (10) of it, almost similar to a Ping-Pong ball hitting the lid of a tin can. However, these vests actually absorb the impact of the (11) bullet spreading its energy around the body (12) rather than been sustained in a single area.(13) Normally, the layers of the vest’s material will stop the bullet from entering the body. However, the vest’s wearer is very likely to sustain bruises (14) and perhaps even internal injuries.Most police officers and military personnel are happy to don their protective clothing as they head out on their assignments. However, they know better than anyone that their safety and security cannot be (15) entrusting completely to their protective gear.Q. (14)The writer is considering deleting the underlined portion. If the writer chooses to delete this phrase, the paragraph would primarily lose a statement that suggests

View answer

Directions:In the passages that follow, some words and phrases are underlined and numbered. In the answer column, you will ﬁnd alternatives for the words and phrases that are underlined. If you think that the original version is best, choose “NO CHANGE,”. You will also ﬁnd questions about a particular section of the passage, or about the entire passage. These questions will be identiﬁed either by an underlined portion or by a number in a box. Look for the answer that clearly expresses the idea, is consistent with the style and tone of the passage, and makes the correct use of standard written English. Read the passage through once before answering the questions. For some questions, you should read beyond the indicated portion before you answer.PassageBody ArmorIf you were an officer of the law or an armed military person, would you prefer to wear a “bullet-proof vest” or “soft body armor” under your (1) suit and uniform?(2) Most often the person would probably opt for the bullet-proof vest, as its name tends to denote a higher level of security. The problem, though, is that no“bullet-proof vest” (3) is really bullet-proof. In fact, there is no protective clothing currently available that offers complete protection from firearms.As weaponry and ammunition have changed through (4) the centuries; so have the materials from which protective clothing is made. During the black powder era of the 1700s, silk (5) was the material of choice to ward off injury or death from a black powder ball. Black powder propelled lead balls were much slower than present-day bullets, and silk was sometimes fairly effective protection against weapons at longer ranges. During World War II, the “flak jacket” was developed as a protective device. (6) Soon, the best this attire could do was to protect the wearer from shrapnel, not from the bullets themselves. (7) Today’s modernprotective vests are made from a variety of synthetic materials, some of which are (8) more with effectiveness than others. The idea is to produce a material that is strong enough to ward off high-speed bullets yet light enough to allow for ease of movement. This can be a daunting task when cost is also considered,(9)Most people have the idea that protective gear causes a bullet to deflect off (10) of it, almost similar to a Ping-Pong ball hitting the lid of a tin can. However, these vests actually absorb the impact of the (11) bullet spreading its energy around the body (12) rather than been sustained in a single area.(13) Normally, the layers of the vest’s material will stop the bullet from entering the body. However, the vest’s wearer is very likely to sustain bruises (14) and perhaps even internal injuries.Most police officers and military personnel are happy to don their protective clothing as they head out on their assignments. However, they know better than anyone that their safety and security cannot be (15) entrusting completely to their protective gear.Q. (3)

View answer

Directions:In the passages that follow, some words and phrases are underlined and numbered. In the answer column, you will ﬁnd alternatives for the words and phrases that are underlined. If you think that the original version is best, choose “NO CHANGE,”. You will also ﬁnd questions about a particular section of the passage, or about the entire passage. These questions will be identiﬁed either by an underlined portion or by a number in a box. Look for the answer that clearly expresses the idea, is consistent with the style and tone of the passage, and makes the correct use of standard written English. Read the passage through once before answering the questions. For some questions, you should read beyond the indicated portion before you answer.PassageBody ArmorIf you were an officer of the law or an armed military person, would you prefer to wear a “bullet-proof vest” or “soft body armor” under your (1) suit and uniform?(2) Most often the person would probably opt for the bullet-proof vest, as its name tends to denote a higher level of security. The problem, though, is that no“bullet-proof vest” (3) is really bullet-proof. In fact, there is no protective clothing currently available that offers complete protection from firearms.As weaponry and ammunition have changed through (4) the centuries; so have the materials from which protective clothing is made. During the black powder era of the 1700s, silk (5) was the material of choice to ward off injury or death from a black powder ball. Black powder propelled lead balls were much slower than present-day bullets, and silk was sometimes fairly effective protection against weapons at longer ranges. During World War II, the “flak jacket” was developed as a protective device. (6) Soon, the best this attire could do was to protect the wearer from shrapnel, not from the bullets themselves. (7) Today’s modernprotective vests are made from a variety of synthetic materials, some of which are (8) more with effectiveness than others. The idea is to produce a material that is strong enough to ward off high-speed bullets yet light enough to allow for ease of movement. This can be a daunting task when cost is also considered,(9)Most people have the idea that protective gear causes a bullet to deflect off (10) of it, almost similar to a Ping-Pong ball hitting the lid of a tin can. However, these vests actually absorb the impact of the (11) bullet spreading its energy around the body (12) rather than been sustained in a single area.(13) Normally, the layers of the vest’s material will stop the bullet from entering the body. However, the vest’s wearer is very likely to sustain bruises (14) and perhaps even internal injuries.Most police officers and military personnel are happy to don their protective clothing as they head out on their assignments. However, they know better than anyone that their safety and security cannot be (15) entrusting completely to their protective gear.Q. (10)

View answer

The period of a simple pendulum T is defined as the amount of time that it takes for a pendulum to swing from one end to the other and back. In studying the period of a simple pendulum, two students express their opinions.Student 1: The period of a pendulum depends on two factors: the mass of the pendulums bob (the object swinging at the end of the pendulum) and the length of the pendulum. The height at which the pendulum is originally dropped does not affect the period T.Student 2: The period of a pendulum T only depends on the length of the pendulum. Varying the mass and the height at which the pendulum is originally dropped does not affect how long the pendulum takes to swing across.The two students ran a series of trials to measure the period of a simple pendulum using varying weights and lengths. The students did not measure height as a factor. The results of the trials can be seen in the table below:Q. During an earthquake, several chandeliers in a mansion begin to swing. Some of the chandeliers are quite small while others, such as one found in the dining room, are very large. However, all of the chandeliers hang the same exact distance from the ceiling. What would the two students predict would happen?

View answer

The period of a simple pendulum T is defined as the amount of time that it takes for a pendulum to swing from one end to the other and back. In studying the period of a simple pendulum, two students express their opinions.Student 1: The period of a pendulum depends on two factors: the mass of the pendulums bob (the object swinging at the end of the pendulum) and the length of the pendulum. The height at which the pendulum is originally dropped does not affect the period T.Student 2: The period of a pendulum T only depends on the length of the pendulum. Varying the mass and the height at which the pendulum is originally dropped does not affect how long the pendulum takes to swing across.The two students ran a series of trials to measure the period of a simple pendulum using varying weights and lengths. The students did not measure height as a factor. The results of the trials can be seen in the table below:Q. On which of the following points would the scientists most likely disagree?

View answer

Top Courses for ACTView all

ACT Mock Test Series 2025

Biology for ACT

How to Prepare for ACT

Mathematics for ACT

Chemistry for ACT

Top Courses for ACT

View all

Two balls are dropped from heights h and 2h respectively. What would be the ratio of times taken by the balls to reach the earth?a)√2 1b)1 √2c)2 1d)4 119Correct answer is option 'B'. Can you explain this answer?

Share with a Friend

Answer this doubt

Question Description
Two balls are dropped from heights h and 2h respectively. What would be the ratio of times taken by the balls to reach the earth?a)√2 1b)1 √2c)2 1d)4 119Correct answer is option 'B'. Can you explain this answer? for ACT 2025 is part of ACT preparation. The Question and answers have been prepared according to the ACT exam syllabus. Information about Two balls are dropped from heights h and 2h respectively. What would be the ratio of times taken by the balls to reach the earth?a)√2 1b)1 √2c)2 1d)4 119Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for ACT 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Two balls are dropped from heights h and 2h respectively. What would be the ratio of times taken by the balls to reach the earth?a)√2 1b)1 √2c)2 1d)4 119Correct answer is option 'B'. Can you explain this answer?.

Solutions for Two balls are dropped from heights h and 2h respectively. What would be the ratio of times taken by the balls to reach the earth?a)√2 1b)1 √2c)2 1d)4 119Correct answer is option 'B'. Can you explain this answer? in English & in Hindi are available as part of our courses for ACT. Download more important topics, notes, lectures and mock test series for ACT Exam by signing up for free.

Here you can find the meaning of Two balls are dropped from heights h and 2h respectively. What would be the ratio of times taken by the balls to reach the earth?a)√2 1b)1 √2c)2 1d)4 119Correct answer is option 'B'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of Two balls are dropped from heights h and 2h respectively. What would be the ratio of times taken by the balls to reach the earth?a)√2 1b)1 √2c)2 1d)4 119Correct answer is option 'B'. Can you explain this answer?, a detailed solution for Two balls are dropped from heights h and 2h respectively. What would be the ratio of times taken by the balls to reach the earth?a)√2 1b)1 √2c)2 1d)4 119Correct answer is option 'B'. Can you explain this answer? has been provided alongside types of Two balls are dropped from heights h and 2h respectively. What would be the ratio of times taken by the balls to reach the earth?a)√2 1b)1 √2c)2 1d)4 119Correct answer is option 'B'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice Two balls are dropped from heights h and 2h respectively. What would be the ratio of times taken by the balls to reach the earth?a)√2 1b)1 √2c)2 1d)4 119Correct answer is option 'B'. Can you explain this answer? tests, examples and also practice ACT tests.

Explore Courses for ACT exam