Tetrahedron on a Spin

Classical Mechanics Level 3

A solid regular tetrahedron:

  • has sides of length 1 m

  • has mass 1 kg

  • is spinning about its symmetry axis at ω \omega = 1 rad/s.

  • has kinetic energy K K Joules

Find 1 K \dfrac{1}{K}


The answer is 40.

Digvijay Singh by Digvijay Singh , 21, India

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1 solution

Md Zuhair
Jan 17, 2018

Hmm

This question can be made tougher if it is given that the tetrahedron is non uniform with some mass distribution.

Never mind, this was uniform ⟹ M . I = m s 2 20 \implies M.I= \dfrac{ms^2}{20}

Just putting into Energy equation of rotational motion, we have

⟹ 1 2 I ω 2 = 1 40 \implies \dfrac{1}{2} I \omega^2 = \dfrac{1}{40}

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The whole point of posting this question was finding moment of inertia of a tetrahedron.

How do you find that?

Digvijay Singh - 3 years, 4 months ago

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Oh. if it was so, then it should be rated to hard or level 4 because its not in JEE Level

Md Zuhair - 3 years, 4 months ago

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This is JEE level. The question appeared on the AITS this weekend, which is a practice test for JEE mains/advance.

Also, I don't get to decide the level of the question. I can't rate it to be level 4

Digvijay Singh - 3 years, 4 months ago

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@Digvijay Singh – Which coaching u study in?

Md Zuhair - 3 years, 4 months ago

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