Irregular block

Classical Mechanics Level 1

A block has edge lengths of 6 cm, 7 cm, and 8 cm (as shown), where opposite faces have the same color. If the block is rolled, which color is most likely to come up on top?

Assume the block's mass is evenly distributed

Inspiration

Each colour is equally likely Blue Red Green

Mahdi Raza by Mahdi Raza , 16, India

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6 solutions

One of the fundamental laws of nature is : Any natural process proceeds in the direction of stable equilibrium by decreasing the Potential Energy . The P. E. of a body is minimum when it's C. G. is closest to ground . In this problem, the C. G. of the body is closest to ground when it rests on the 7 × 8 7\times 8 face. Hence the color showing up will be Green .

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Hana Wehbi
Jun 7, 2020

The area of the green part is the highest so the probability of landing on green is most likely.

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Green has the most area, 8×7, so it'll likely land on the green base, opposite to that is also green, which will be on top.

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Krishna Karthik
Jun 8, 2020

Most area is taken up by green, 7 x 8.

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Joshua Olayanju
Jun 8, 2020

The way I think of it is that when you are flipping the cube. The side with the largest area would be the side it would land on. Since it also the same color on the opposite side I knew that green would also be facing up

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Aryan Sanghi
Jun 7, 2020

Equilibrium is favoured towards 8×7 cm side. So, it is more likely to show up, which means the answer is g r e e n \boxed{green}

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