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everyone. This is concern number thirty one from chapter five. So this objects that this problem says the two objects lure each other gravitationally with force of two allude five time ten to the minus ten Newton's when there's your point two 5 meters apart, their full masses 4 kilograms find their individual masses So new start, yet of detect the masses. So you'd to speak the M one equals and and then we can define that. Since we're going come a complete value, we deserve to say that em too, equals four kilograms minus. And and that's just from the truth that em one plus the too, equates to four. And also we characterized m one as simply normal tiny m so subtracted end m 2 eagles because that months. Castle too. 4 months and one pardon me. Okay, so us can likewise see that these air suggest masses since we have actually an equation because that that. So gravitational pressure is equal to the take gravity consistent and want them to over r squared. And also that's just, um, that's one equation that we have actually for the gravitational force between two suggest masses with a radius of our separating them. Okay, so currently we change I'm one of them too. With the worths we have so g we're gonna have m times because that kilograms minus one eye over r squared. So now we square us multiply m to the four and the m squared and also we end up with the gravitational constant six suggest six seven times ten to the minus eleven noon meter squared every killing ground time for, um minus and squared end r squared zero suggest two 5 meters square. And also that is equal to no too quiet. Five times ten to the minus ten news that's offered the equation. Okay, so currently we can rearrange this and also solve gaining a quadratic equation. Okay, so we divide, um, we divide, Yeah, us multiply em over to we multiply the molecule the denominator end to the various other side and also divide by and divide through six suggest six seven and then us just included back over. Okay, for this reason the equation that you finish up getting I'm no going come go with the algebra of it. But you finish up getting m squared minus for M add to zero allude two three four equal zero. Okay, therefore three right there. I'm squared minus because that M plus zero allude two three four Equal zero means Do the quadratic equation an unfavorable B minus four. So four plus or minus the square root of B squared minus four times a cz one C zero suggest two three four over come A, i m sorry is simply two times one end two and you native this add to or minus.

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You gain two values, which room our masses so and won equals three suggest nine 4 kilograms, and I'm too equals zero allude of 6 kilograms. And also of course, girlfriend can inspect by adding these, and they will include up come four.