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Center of mass of uniformly distributed mass

The position of the centre of mass of a uniform semicircular w

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The position of the centre of mass of a uniform semicircular wire of radius 'R' placed in x-y plane with its centre at the origin and the line joining its ends as x-axis is given by $(0, \frac{x R}{π})$ . Then, the value of |x| is _____,

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Exam:

JEE Mains 2021 July 22 Shift 2

Text solutionVerified

To find

y_{c m}

we use

y_{c m} = \frac{1}{M} \int d m y

......(i)

Here for dm we consider an elemental arc of the ring at an angle

θ

from the x-direction of angular width de. If radius of the ring is R then its y coordinate will be

R sin θ

, here d m is given as

dm = \frac{M}{π R} \times R d θ

So from equation ....(i), we have

y_{c m} = \frac{1}{M} \int_{0}^{π} \frac{M}{π R} R d θ (R sin θ) = \frac{R}{π} \int_{0}^{π} sin θ d θ

y_{c m} = \frac{2 R}{π}

......(2)

∴ x = 2

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The position of the centre of mass of a uniform semicircular wire of radius 'R' placed in x-y plane with its centre at the origin and the line joining its ends as x-axis is given by

(0, \frac{x R}{π})

. Then, the value of |x| is _____,

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Question Text	The position of the centre of mass of a uniform semicircular wire of radius 'R' placed in x-y plane with its centre at the origin and the line joining its ends as x-axis is given by $(0, \frac{x R}{π})$ . Then, the value of \|x\| is _____,
Topic	System of Particles and Rotational Motion
Subject	Physics
Class	Class 11
Answer Type	Text solution:1
Upvotes	93

The position of the centre of mass of a uniform semicircular wire of radius 'R' placed in x-y plane with its centre at the origin and the line joining its ends as x-axis is given by $(0, \frac{x R}{π})$ . Then, the value of |x| is _____,

Text solutionVerified

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The position of the centre of mass of a uniform semicircular wire of radius 'R' placed in x-y plane with its centre at the origin and the line joining its ends as x-axis is given by $(0, \frac{x R}{π})$ . Then, the value of |x| is _____,