A rigid bar (negligible mass) of leng...

Question

A rigid bar (negligible mass) of length 80 cm connects a large sphere with a mass (m₁) of 25 g to a small sphere with an unknown mass (m₂). The large sphere is located at one end of the bar, with the center of mass of the bar located 22 cm away from this sphere. Determine the mass of the sphere (in grams) at the other end of the bar.

Accepted Answer

Perform complete factorization of the given expression or categorize it as the prime polynomial where we have 6 48 into the third minus 3 75 into the third. So 6 48 the third minus 3 75 into the third. To start this off, we can factor out a three from both terms Because both are divisible by three. Back out the three off. The first one, we get 2:16 into the third. Uh The other one, the second one, you get 1 25 in the third. Now that we're here, we can factor out this polynomial right here to do this. We'll make use of the difference of cubes. The difference of cubes states that if we have some expression X to the third minus Y to the third, the equivalent factor this given by X minus Y multiplied by X squared plus X Y minus Y square made that plus Y squared actually. So we can change this form into this other form on the right here. Now, if you look at our original problem, three, 216 is the same thing as saying 6th to the 3rd. So you can write this at six am to the third. So for the end, we have five in for the third, we can now rewrite in our form, You will get three times six M -5 n multiplied bye six M squared plus six M times five N plus five N squared. Three, multiplied by six M minus five M is also multiplied thin by 36 M squared Plus 30 MN Plus 25 in square. We can't simplify any further. So we have the results of our factor here. If you look over at our possible answers, we can then determine the answer to our problem is answer B OK. I hope to help you solve the problem. Thank you for watching. Goodbye.

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