Question

Ingum "
Two wheels of M.I. 3kg mº and 5kg ma
rotating at the rate of 600 rpm and 800 m
respectively in the same direction. If the two
are coupled so as to rotate with the same axis of
rotation, the resultant speed of rotation will be
(in rpm)
1) 725 2) 850 3) 420 4) 630​

Answer 1

$\huge\underline\mathfrak\red{Answer}$

$m.i(1) = 3kg {m}^{2} \\ initial \: angular \: speed(1) = 600rpm\\ \\ m.i(2) =5kg {m}^{2} \\ initial \: ANGULAR \: speed (2)= 800rpm \\ \\ acc \: to \: law \: of \: conversion \: of \: angular \\ momentum..... \\ \\ m.i(1) \times w(1) + m.i(2) \times w(2) \\ \\ always \: equals \\ \\ m.i(1) \times w(3) + m.i(2) \times w(4) \\ \\ now \: when \: two \: body \: coupled \: than \\ resultant \: m.i \: is \: the \: some \: of \: their \\ individual \: m.i \\ \\ 3 \times 600 + 5 \times 800 = x(5 + 3) \\ \\ where \: x \: is \: the \: resultant \: speed \: \\ after \: coupling \\ \\ 1800 + 4000 = 8x \\ \\ </strong><strong>5</strong><strong>8</strong><strong>00 = 8x \\ \\ x = \frac{</strong><strong>5</strong><strong>8</strong><strong>00}{8} \\ \\ x = </strong><strong>7</strong><strong>2</strong><strong>5</strong><strong>rpm$

Answer 2

The resultant speed of rotation is 725 rpm.

(1) is correct option

Explanation:

Given that,

Moment of inertia =  3 kg m²

Moment of inertia = 5 kg m²

Rate = 600 rpm

Distance = 800 m

We need to calculate the resultant speed of rotation

Using formula of moment of inertia

$I\omega=I_{1}\omega_{1}+I_{2}\omega_{2}$

Put the value into the formula

$(3+5)\omega=3\times600+5+800$

$\omega=\dfrac{1800+4000}{8}$

$\omega=725\ rpm$

Hence, The resultant speed of rotation is 725 rpm.

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Topic : moment of inertia

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