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In an epicyclic gear train, an arm carries two gears A and B having 36 and 45 teeth respectively. If the arm rotates at 150 r.p. m. in the anticlockwise direction about the centre of the gear A which is fixed, determine the speed of gear B. If the gear A instead of being fixed, makes 300 r.p.m. in the clockwise direction, what will be the speed of gear B?
- a)510 rpm, counter-clockwise
- b)350 rpm, clockwise
- c)510 rad/s, clockwise
- d)350 rpm, counter-clockwise
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
In an epicyclic gear train, an arm carries two gears A and B having 36...
Let
NA = Speed of gear A
NB = Speed of gear B, and
NC = Speed of arm C
Assuming the arm C to be fixed, speed of gear A relative to arm C
= NA − NC
and speed of gear B relative to arm
C = NB − NC
since the gears A and B revolve in opposite directions, therefore
Speed of gear B when gear A is fixed
When gear A is fixed, the arm rotates at 150 r.p.m. in the anticlockwise direction, i.e.
NA = 0, and NC = +150r⋅p⋅m
or NB = −150 × −0.8 + 150 = 120 + 150 = 270r⋅p⋅m⋅ Ans.
Speed of gear B when gear A makes 300 r.p.m. clockwise
since the gear A makes 300 r.p.m. clockwise, therefore
NA = −300r⋅p⋅m
NB = -450 x -0.8 + 150 = 360 + 150 = 510 r.pm. Ans
Most Upvoted Answer
In an epicyclic gear train, an arm carries two gears A and B having 36...
Given data:
Gear A: 36 teeth
Gear B: 45 teeth
Arm rotation speed: 150 rpm (anticlockwise)
To find:
Speed of gear B
Solution:
1. Number of teeth in each gear represents the gear ratio. Therefore, gear ratio of gear A = 36 and gear ratio of gear B = 45.
2. In an epicyclic gear train, the speed ratio is given by the formula:
Speed ratio = (1 + (z2/z1)) where z1 is the number of teeth in the smaller gear and z2 is the number of teeth in the larger gear.
3. For this problem, gear A is the smaller gear and gear B is the larger gear. Therefore, the speed ratio is:
Speed ratio = (1 + (45/36)) = 2.25
4. The arm rotation speed is the speed of gear A. Therefore, the speed of gear B can be calculated using the formula:
Speed of B = (Speed of A)/(Speed ratio)
5. Substituting the given values, we get:
Speed of B = (150 rpm)/(2.25) = 66.67 rpm
6. If gear A rotates at 300 rpm in the clockwise direction, the speed of gear B can be calculated using the same formula:
Speed ratio = (1 + (45/36)) = 2.25
Speed of B = (Speed of A)/(Speed ratio) = (300 rpm)/(2.25) = 133.33 rpm
7. However, the question asks for the direction of rotation of gear B. The direction of rotation of gear B is opposite to the direction of rotation of gear A. Therefore, if gear A rotates clockwise, gear B will rotate in the counter-clockwise direction.
Therefore, the final answer is option 'A' - 510 rpm, counter-clockwise.
Gear A: 36 teeth
Gear B: 45 teeth
Arm rotation speed: 150 rpm (anticlockwise)
To find:
Speed of gear B
Solution:
1. Number of teeth in each gear represents the gear ratio. Therefore, gear ratio of gear A = 36 and gear ratio of gear B = 45.
2. In an epicyclic gear train, the speed ratio is given by the formula:
Speed ratio = (1 + (z2/z1)) where z1 is the number of teeth in the smaller gear and z2 is the number of teeth in the larger gear.
3. For this problem, gear A is the smaller gear and gear B is the larger gear. Therefore, the speed ratio is:
Speed ratio = (1 + (45/36)) = 2.25
4. The arm rotation speed is the speed of gear A. Therefore, the speed of gear B can be calculated using the formula:
Speed of B = (Speed of A)/(Speed ratio)
5. Substituting the given values, we get:
Speed of B = (150 rpm)/(2.25) = 66.67 rpm
6. If gear A rotates at 300 rpm in the clockwise direction, the speed of gear B can be calculated using the same formula:
Speed ratio = (1 + (45/36)) = 2.25
Speed of B = (Speed of A)/(Speed ratio) = (300 rpm)/(2.25) = 133.33 rpm
7. However, the question asks for the direction of rotation of gear B. The direction of rotation of gear B is opposite to the direction of rotation of gear A. Therefore, if gear A rotates clockwise, gear B will rotate in the counter-clockwise direction.
Therefore, the final answer is option 'A' - 510 rpm, counter-clockwise.
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In an epicyclic gear train, an arm carries two gears A and B having 36 and 45 teeth respectively. If the arm rotates at 150 r.p. m. in the anticlockwise direction about the centre of the gear A which is fixed, determine the speed of gear B. If the gear A instead of being fixed, makes 300 r.p.m. in the clockwise direction, what will be the speed of gear B?a)510 rpm, counter-clockwiseb)350 rpm, clockwisec)510 rad/s, clockwised)350 rpm, counter-clockwiseCorrect answer is option 'A'. Can you explain this answer?
Question Description
In an epicyclic gear train, an arm carries two gears A and B having 36 and 45 teeth respectively. If the arm rotates at 150 r.p. m. in the anticlockwise direction about the centre of the gear A which is fixed, determine the speed of gear B. If the gear A instead of being fixed, makes 300 r.p.m. in the clockwise direction, what will be the speed of gear B?a)510 rpm, counter-clockwiseb)350 rpm, clockwisec)510 rad/s, clockwised)350 rpm, counter-clockwiseCorrect answer is option 'A'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about In an epicyclic gear train, an arm carries two gears A and B having 36 and 45 teeth respectively. If the arm rotates at 150 r.p. m. in the anticlockwise direction about the centre of the gear A which is fixed, determine the speed of gear B. If the gear A instead of being fixed, makes 300 r.p.m. in the clockwise direction, what will be the speed of gear B?a)510 rpm, counter-clockwiseb)350 rpm, clockwisec)510 rad/s, clockwised)350 rpm, counter-clockwiseCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In an epicyclic gear train, an arm carries two gears A and B having 36 and 45 teeth respectively. If the arm rotates at 150 r.p. m. in the anticlockwise direction about the centre of the gear A which is fixed, determine the speed of gear B. If the gear A instead of being fixed, makes 300 r.p.m. in the clockwise direction, what will be the speed of gear B?a)510 rpm, counter-clockwiseb)350 rpm, clockwisec)510 rad/s, clockwised)350 rpm, counter-clockwiseCorrect answer is option 'A'. Can you explain this answer?.
In an epicyclic gear train, an arm carries two gears A and B having 36 and 45 teeth respectively. If the arm rotates at 150 r.p. m. in the anticlockwise direction about the centre of the gear A which is fixed, determine the speed of gear B. If the gear A instead of being fixed, makes 300 r.p.m. in the clockwise direction, what will be the speed of gear B?a)510 rpm, counter-clockwiseb)350 rpm, clockwisec)510 rad/s, clockwised)350 rpm, counter-clockwiseCorrect answer is option 'A'. Can you explain this answer? for GATE 2024 is part of GATE preparation. The Question and answers have been prepared according to the GATE exam syllabus. Information about In an epicyclic gear train, an arm carries two gears A and B having 36 and 45 teeth respectively. If the arm rotates at 150 r.p. m. in the anticlockwise direction about the centre of the gear A which is fixed, determine the speed of gear B. If the gear A instead of being fixed, makes 300 r.p.m. in the clockwise direction, what will be the speed of gear B?a)510 rpm, counter-clockwiseb)350 rpm, clockwisec)510 rad/s, clockwised)350 rpm, counter-clockwiseCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for GATE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for In an epicyclic gear train, an arm carries two gears A and B having 36 and 45 teeth respectively. If the arm rotates at 150 r.p. m. in the anticlockwise direction about the centre of the gear A which is fixed, determine the speed of gear B. If the gear A instead of being fixed, makes 300 r.p.m. in the clockwise direction, what will be the speed of gear B?a)510 rpm, counter-clockwiseb)350 rpm, clockwisec)510 rad/s, clockwised)350 rpm, counter-clockwiseCorrect answer is option 'A'. Can you explain this answer?.
Solutions for In an epicyclic gear train, an arm carries two gears A and B having 36 and 45 teeth respectively. If the arm rotates at 150 r.p. m. in the anticlockwise direction about the centre of the gear A which is fixed, determine the speed of gear B. If the gear A instead of being fixed, makes 300 r.p.m. in the clockwise direction, what will be the speed of gear B?a)510 rpm, counter-clockwiseb)350 rpm, clockwisec)510 rad/s, clockwised)350 rpm, counter-clockwiseCorrect answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for GATE.
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ample number of questions to practice In an epicyclic gear train, an arm carries two gears A and B having 36 and 45 teeth respectively. If the arm rotates at 150 r.p. m. in the anticlockwise direction about the centre of the gear A which is fixed, determine the speed of gear B. If the gear A instead of being fixed, makes 300 r.p.m. in the clockwise direction, what will be the speed of gear B?a)510 rpm, counter-clockwiseb)350 rpm, clockwisec)510 rad/s, clockwised)350 rpm, counter-clockwiseCorrect answer is option 'A'. Can you explain this answer? tests, examples and also practice GATE tests.
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