### Video Transcript

everyone. This is inquiry number thirty one from chapter five. Therefore this objects the this difficulty says the two objects lure each various other gravitationally with force of two point five times ten to the minus ten Newton's as soon as there's your allude two five meters apart, their total masses 4 kilograms find their individual masses So brand-new start, yet of recognize the masses. So you'd speak the M one equals and and then we can specify that. Since we're going come a full value, we have the right to say that em too, amounts to four kilograms minus. And also and that's just from the reality that em one plus the too, equates to four. And also we identified m one as simply normal small m for this reason subtracted end m 2 eagles because that months. Them too. 4 months and one excuse me. Okay, so us can likewise see the these air point masses since we have actually an equation because that that. So gravitational pressure is same to the take gravity consistent and desire them to end r squared. And that's just, um, that's an equation that we have actually for the gravitational force in between two suggest masses with a radius of ours separating them. Okay, so now we change I'm one of them too. With the values we have so g we're gonna have actually m times because that kilograms minus one eye over r squared. So currently we square we multiply m to the four and the m squared and also we end up through the gravitational consistent six suggest six seven times ten to the minus eleven noon meters squared per killing ground times for, um minus and squared end r squared zero point two 5 meters square. And also that is equal to no as well quiet. Five times ten to the minus ten news that's offered the equation. Okay, so now we can rearrange this and also solve getting a quadratic equation. Okay, so we divide, um, us divide, Yeah, we multiply em end to we multiply the molecule the denominator over to the other side and divide by and divide through six allude six seven and also then we just included back over. Okay, therefore the equation that you finish up obtaining I'm not going come go through the algebra that it. However you end up gaining m squared minus because that M add to zero allude two three 4 equal zero. Okay, therefore three best there. I'm squared minus because that M to add zero point two three 4 Equal zero means Do the quadratic equation an adverse B minus four. So four plus or minus the square root of B squared minus 4 times a cz one C zero allude two three 4 over come A, which is just two times one over two and you native this plus or minus.

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You acquire two values, which room our masses so and won equates to three allude nine 4 kilograms, and also I'm too equals zero point of six kilograms. And also of course, friend can inspect by including these, and they will add up to four.