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A wheel initially at rest ,is rotated with uniform angular acceleration .The wheel rotates through an angle a1 in first one second and through an additional angle a2 in the next one second .The ratio a2/a1 is a) 4. b) 2. c) 3. d) 1 answer given is (c) explain [iitjee-1987]?
Most Upvoted Answer
? A wheel initially at rest ,is rotated with uniform angular accelerat...
Here,
initial angular velocity = 0m/s.
angular acceleration = A rad/s^2
angular disp. = wt + 1/2At^2
a1 = 0 + 1/2*A(1)^2. (as t = 1s)
a1 = 1/2*A
now, when t=2s
a' = 0 + 1/2*A(2)^2
a' = 1/2*4A
a' = 2A
therefore,
a2 = a' - a1
a2 = 2A - A/2
a2 = 3A/2
so now,
a2/a1 = 3/2A ÷ A/2
therefore,
a2/a1 = 3
Hope it helps.
initial angular velocity = 0m/s.
angular acceleration = A rad/s^2
angular disp. = wt + 1/2At^2
a1 = 0 + 1/2*A(1)^2. (as t = 1s)
a1 = 1/2*A
now, when t=2s
a' = 0 + 1/2*A(2)^2
a' = 1/2*4A
a' = 2A
therefore,
a2 = a' - a1
a2 = 2A - A/2
a2 = 3A/2
so now,
a2/a1 = 3/2A ÷ A/2
therefore,
a2/a1 = 3
Hope it helps.
Community Answer
? A wheel initially at rest ,is rotated with uniform angular accelerat...
Problem:
A wheel initially at rest is rotated with uniform angular acceleration. The wheel rotates through an angle a1 in the first one second and through an additional angle a2 in the next one second. Find the ratio a2/a1.
Solution:
Let's assume the initial angular velocity of the wheel is ω0 and the angular acceleration is α.
Step 1: Finding the angular velocity after 1 second
Using the equation of motion for rotational motion:
ω = ω0 + αt
After 1 second, ω1 = ω0 + α(1) = ω0 + α
Step 2: Finding the angle rotated in the first second (a1)
Using the equation for angular displacement:
θ = ω0t + (1/2)αt^2
Substituting the values, we get:
a1 = ω0(1) + (1/2)α(1)^2
= ω0 + (1/2)α
Step 3: Finding the angular velocity after 2 seconds
Using the equation of motion for rotational motion:
ω = ω0 + αt
After 2 seconds, ω2 = ω0 + α(2) = ω0 + 2α
Step 4: Finding the angle rotated in the second second (a2)
Using the equation for angular displacement:
θ = ω0t + (1/2)αt^2
Substituting the values, we get:
a2 = ω0(1) + (1/2)α(2)^2
= ω0 + 2α
Step 5: Finding the ratio a2/a1
Dividing a2 by a1:
a2/a1 = (ω0 + 2α)/(ω0 + (1/2)α)
Simplifying the expression:
a2/a1 = (2(ω0 + α))/(ω0 + (1/2)α)
= 2(1 + α/ω0)/(1 + (1/2)(α/ω0))
Since the wheel is initially at rest, ω0 = 0. Therefore, α/ω0 is undefined. Hence, we cannot determine the exact value of a2/a1.
Therefore, the given answer (c) is incorrect. The correct answer should be undefined.
A wheel initially at rest is rotated with uniform angular acceleration. The wheel rotates through an angle a1 in the first one second and through an additional angle a2 in the next one second. Find the ratio a2/a1.
Solution:
Let's assume the initial angular velocity of the wheel is ω0 and the angular acceleration is α.
Step 1: Finding the angular velocity after 1 second
Using the equation of motion for rotational motion:
ω = ω0 + αt
After 1 second, ω1 = ω0 + α(1) = ω0 + α
Step 2: Finding the angle rotated in the first second (a1)
Using the equation for angular displacement:
θ = ω0t + (1/2)αt^2
Substituting the values, we get:
a1 = ω0(1) + (1/2)α(1)^2
= ω0 + (1/2)α
Step 3: Finding the angular velocity after 2 seconds
Using the equation of motion for rotational motion:
ω = ω0 + αt
After 2 seconds, ω2 = ω0 + α(2) = ω0 + 2α
Step 4: Finding the angle rotated in the second second (a2)
Using the equation for angular displacement:
θ = ω0t + (1/2)αt^2
Substituting the values, we get:
a2 = ω0(1) + (1/2)α(2)^2
= ω0 + 2α
Step 5: Finding the ratio a2/a1
Dividing a2 by a1:
a2/a1 = (ω0 + 2α)/(ω0 + (1/2)α)
Simplifying the expression:
a2/a1 = (2(ω0 + α))/(ω0 + (1/2)α)
= 2(1 + α/ω0)/(1 + (1/2)(α/ω0))
Since the wheel is initially at rest, ω0 = 0. Therefore, α/ω0 is undefined. Hence, we cannot determine the exact value of a2/a1.
Therefore, the given answer (c) is incorrect. The correct answer should be undefined.
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? A wheel initially at rest ,is rotated with uniform angular acceleration .The wheel rotates through an angle a1 in first one second and through an additional angle a2 in the next one second .The ratio a2/a1 is a) 4. b) 2. c) 3. d) 1 answer given is (c) explain [iitjee-1987]?
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? A wheel initially at rest ,is rotated with uniform angular acceleration .The wheel rotates through an angle a1 in first one second and through an additional angle a2 in the next one second .The ratio a2/a1 is a) 4. b) 2. c) 3. d) 1 answer given is (c) explain [iitjee-1987]? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about ? A wheel initially at rest ,is rotated with uniform angular acceleration .The wheel rotates through an angle a1 in first one second and through an additional angle a2 in the next one second .The ratio a2/a1 is a) 4. b) 2. c) 3. d) 1 answer given is (c) explain [iitjee-1987]? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for ? A wheel initially at rest ,is rotated with uniform angular acceleration .The wheel rotates through an angle a1 in first one second and through an additional angle a2 in the next one second .The ratio a2/a1 is a) 4. b) 2. c) 3. d) 1 answer given is (c) explain [iitjee-1987]?.
? A wheel initially at rest ,is rotated with uniform angular acceleration .The wheel rotates through an angle a1 in first one second and through an additional angle a2 in the next one second .The ratio a2/a1 is a) 4. b) 2. c) 3. d) 1 answer given is (c) explain [iitjee-1987]? for NEET 2024 is part of NEET preparation. The Question and answers have been prepared according to the NEET exam syllabus. Information about ? A wheel initially at rest ,is rotated with uniform angular acceleration .The wheel rotates through an angle a1 in first one second and through an additional angle a2 in the next one second .The ratio a2/a1 is a) 4. b) 2. c) 3. d) 1 answer given is (c) explain [iitjee-1987]? covers all topics & solutions for NEET 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for ? A wheel initially at rest ,is rotated with uniform angular acceleration .The wheel rotates through an angle a1 in first one second and through an additional angle a2 in the next one second .The ratio a2/a1 is a) 4. b) 2. c) 3. d) 1 answer given is (c) explain [iitjee-1987]?.
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