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An inclined plane makes an angle of 30o with the horizontal. A solid sphere rolling down this inclined plane from rest without slipping has a linear acceleration equal to
- a)g/3
- b)2g/3
- c)5g/7
- d)5g/14
Correct answer is option 'D'. Can you explain this answer?
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Verified Answer
An inclined plane makes an angle of 30o with the horizontal. A solid s...
net force on center of mass = mgsin@
friction force = f (acting upwards)
for linear motion ,
mgsin@ - f = ma ....1
for angular motion
fR = I(alfa) ..2 (alfa is angular accleration)
from 1 & 2
mgsin@ = ma + I(alfa)/R ...3
now, if it is given that the body is rolling without slipping then we apply a = (alfa)R
now eq 3 becomes
mgsin@ = ma + 2ma/5 (Isphere = 2mR^2/5)
a = 5gsin@/7
=5g/14 (sin30 = 1/2)
Most Upvoted Answer
An inclined plane makes an angle of 30o with the horizontal. A solid s...
Solution:
Given: Angle of inclined plane, θ = 30°
As the sphere is rolling without slipping on an inclined plane, the linear acceleration of the sphere a can be given by:
a = (2/3) g sin θ
where g is the acceleration due to gravity and θ is the angle made by the inclined plane with the horizontal.
Substituting the values, we get:
a = (2/3) x 9.8 x sin 30°
a = 3.27 m/s2
Therefore, the correct answer is option D, which is 5g/14.
Reasoning:
The acceleration of the sphere rolling down an inclined plane is determined by the angle made by the inclined plane with the horizontal, as well as the acceleration due to gravity. The linear acceleration of the sphere is given by the formula a = (2/3) g sin θ, where θ is the angle made by the inclined plane with the horizontal. Substituting the values, we get the correct answer as 5g/14.
Given: Angle of inclined plane, θ = 30°
As the sphere is rolling without slipping on an inclined plane, the linear acceleration of the sphere a can be given by:
a = (2/3) g sin θ
where g is the acceleration due to gravity and θ is the angle made by the inclined plane with the horizontal.
Substituting the values, we get:
a = (2/3) x 9.8 x sin 30°
a = 3.27 m/s2
Therefore, the correct answer is option D, which is 5g/14.
Reasoning:
The acceleration of the sphere rolling down an inclined plane is determined by the angle made by the inclined plane with the horizontal, as well as the acceleration due to gravity. The linear acceleration of the sphere is given by the formula a = (2/3) g sin θ, where θ is the angle made by the inclined plane with the horizontal. Substituting the values, we get the correct answer as 5g/14.
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An inclined plane makes an angle of 30o with the horizontal. A solid sphere rolling down this inclined plane from rest without slipping has a linear acceleration equal toa)g/3b)2g/3c)5g/7d)5g/14Correct answer is option 'D'. Can you explain this answer?
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An inclined plane makes an angle of 30o with the horizontal. A solid sphere rolling down this inclined plane from rest without slipping has a linear acceleration equal toa)g/3b)2g/3c)5g/7d)5g/14Correct answer is option 'D'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about An inclined plane makes an angle of 30o with the horizontal. A solid sphere rolling down this inclined plane from rest without slipping has a linear acceleration equal toa)g/3b)2g/3c)5g/7d)5g/14Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An inclined plane makes an angle of 30o with the horizontal. A solid sphere rolling down this inclined plane from rest without slipping has a linear acceleration equal toa)g/3b)2g/3c)5g/7d)5g/14Correct answer is option 'D'. Can you explain this answer?.
An inclined plane makes an angle of 30o with the horizontal. A solid sphere rolling down this inclined plane from rest without slipping has a linear acceleration equal toa)g/3b)2g/3c)5g/7d)5g/14Correct answer is option 'D'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about An inclined plane makes an angle of 30o with the horizontal. A solid sphere rolling down this inclined plane from rest without slipping has a linear acceleration equal toa)g/3b)2g/3c)5g/7d)5g/14Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for An inclined plane makes an angle of 30o with the horizontal. A solid sphere rolling down this inclined plane from rest without slipping has a linear acceleration equal toa)g/3b)2g/3c)5g/7d)5g/14Correct answer is option 'D'. Can you explain this answer?.
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