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patriot [66]
3 years ago
13

A piece of thin uniform wire of mass m and length 3b is bent into an equilaeral triangle.

Physics
1 answer:
Nookie1986 [14]3 years ago
4 0

Answer: Option (C) is the correct answer.

Explanation:

Formula for moment of inertia is as follows.

                 M.I = \frac{mass \times (length)^{2}}{3}

Hence, moment of inertia of two rods is as follows.

      M.I of two rods = 2 \times \frac{(\frac{m}{3} \times b^{2})}{3}

                                = \frac{2mb^{2}}{9}    

As third rod have no connection with vertices. So, moment of inertia of a rod along an axis passing through its center is as follows.

           M.I = \frac{mass \times (length)^{2}}{12}

                 = \frac{mb^{2}}{3 \times 12}

                 = \frac{mb^{2}}{36}

Using parallel axis theorem moment of inertia through vertices is as follows.

  \frac{mb^{2}}{36} + mass \times \text{distance between the two axes}

       h^{2} = b^{2} - \frac{b^{2}}{4}

                  = \frac{3b^{2}}{4}

                h = \frac{\sqrt{3b}}{2}

Now, we will calculate the moment of inertia of third rod about vertices is as follows.

        \frac{mb^{2}}{36} + [(\frac{m}{3}) \times 3\frac{b^{2}}{4}]

            = mb^{2}[\frac{1}{36} + \frac{1}{4}]

            = 5 \frac{mb^{2}}{18}

Therefore, total moment of inertia is calculated as follows.

            Total M.I = \frac{2mb^{2}}{9} + \frac{5mb^{2}}{18}

                            = \frac{mb^{2}}{2}

Thus, we can conclude that the moment of inertia of the wire triangle about an axis perpendicular to the plane of the triangle and passing through one of its vertices is \frac{mb^{2}}{2}.

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fiasKO [112]

Answer:

35000 KJ

Explanation:

The equation for the kinetic energy is given by the formula :

E_{k} = \frac{1}{2} mv^{2}

E_{k} = \frac{1}{2} (700)(10)^{2}

E_{k} = \frac{1}{2} (700)(100)

E_{k} = (350)(100)  OR E_{k} = \frac{1}{2} (70000)

E_{k} = 35000

Units will be kilojoules since the units of mass was kilograms .

Our final answer is 35000 KJ

Hope this helped and have a good day

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Gut microbiota vary greatly amongst laboratory animals, and these differences result in notable differences in experimental results. Mice of the same strain from different vendors have different microbiota profiles (17), and similarly, the same mice housed at different institutions have different microbiota profiles (18, 19). Conversely, inoculating two different inbred mouse strains with the same gut bacteria leads to differences in host gene expression between the two mouse strains (20). Clearly, there is a complex interplay between the genetics of the microbiota and that of the host organism, which has only recently begun to be appreciated.

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Examples in the literature have highlighted the important and unexpected ways in which gut microbiota can affect a variety of experimental parameters. In a series of studies, Vijay-Kumar et al. (13, 21) reported that although TLR5 null animals initially had a colitis phenotype, when these mice were “rederived” and their gut microbiota altered, the colitis phenotype was greatly attenuated, and instead the null animals exhibited metabolic syndrome. In addition, Lathrop et al. put forward a model by which T-cells are educated not only by self/non-self mechanisms, but also by microbiota-derived “non-self” antigens (22). Accordingly, they found that the presence or absence of microbiota determined whether T cells would induce colitis in mice. Finally, Yang et al. reported that when the same knockout mice were housed at two different institutions, they had markedly different microbiota profiles – and the mice at one institution (MIT) were quite susceptible to colitis, whereas mice at the other institution (MHH) failed to develop any significant pathology under the same conditions (19). Unequivocally, altering gut microbiota – even by housing animals at different institutions – can have dramatic effects on the phenotype observed.

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Gut Microbiota and Obesity and Diabetes

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