A uniform rod is 2.00 m long and has mass 1.80 kg. A 2.40-kg clamp is attached to the rod. How far should the center of gravity of the clamp be from the left-hand end of the rod in order for the center of gravity of the composite object to be 1.20 m from the left-hand end of the rod?

Video transcript

Everyone in this problem. We have a 500 g hollow sphere attached to a uniform metallic stick of mass. one kg in length one m. The sphere can slide freely along the stick initially the stick lies along the X axis. Suppose you set the sphere at distance X from the right hand end of the stick. Okay, we're asked to find X if the position of the center of mass of the composite system is 36 cm from the right hand end. Alright, so we have our stick here and along the X axis and then we kind of have a sphere that's allowed to slide along it. Okay, the distance the center of the sphere from the right hand N is going to be X. Okay, the length of our stick is one m and it has a mass M of one kg in the mass of the sphere. We'll call it M two, we'll call the mass of the stick. Em one the mass of the spear is going to be g Which is equal to 500 g times one kg per 1000 g. Okay, so we divide by 1000 to get 0.5 kg. Alright, so we have essentially distances. Okay we have information about mass. Okay, we have information about center of mass. So let's go ahead and use the center of mass equation. Okay and we have the X center of mass is equal to M one X one plus M two X two. Okay, we have two objects. We have our stick and we have our sphere So we have two things in our equation divided by the sum of the masses. M one M two. Okay, so recall the center of mass equation. Now, what we're trying to find is this distance X two. Okay. Which is a distance from the right end to the sphere? So we're trying to find this distance X two. Alright, so our center of mass we're told in the problem is centimeters. Okay, we have 36 centimeters which is going to be equal to centimeters? Times one m per 100 centimeters. Okay, we divide by 100 we get 0.36 m. Okay, so we want everything in our standard unit. So we convert our centimeters to meters. We get 0.36 m is equal to the mass of the stick. one kg Times the distance from the right end while the stick, the center of mass of the stick is halfway because it's a uniform or told it's a uniform. So this is going to be 0.5 m. Then we have the mass of our sphere which is 0.5 kg times the distance X two that we're looking for divided by the sum of the masses one kg plus 0.5 kg. Okay, Now we filled in all of the information. The only thing we don't know is X two. So we can go ahead and solve. Now we get okay, we get 0.36 m. Okay, multiplying both sides by this one kg plus 0. kg. So we have times 1.5 kg is equal to one kg times 10.5 m is going to be 0.5 kilogram meters plus 0.5 kg times X two. So we get that X is going to be equal to 0.36 m times 1.5 kg is 0.54 unit kilogram meter. Okay, We're going to subtract the 0.5 kilogram meter. Okay? And then we have to divide by 0.5 kg. This is gonna leave us with a unit of meter, which is a unit. We want four distance. Okay, so our units check out. We get 0.0 eight m. Now we see that the answer choices are in centimeters. Okay, So we're gonna multiply this by 100 centimeters per meter in the unit of meter cancels. And we're left with eight centimeters. Okay? Alright, So let's go back up to our answer choices and we found that the distance X from the right hand end of the stick of the sphere should be eight centimeters which is answer. B. Thanks everyone for watching. I hope this video helped see you in the next one