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Problem 25 Easy Difficulty

ssm A bowling ball (mass $=7.2 \mathrm{kg},$ radius $=0.11 \mathrm{m} )$ and a billiard ball (mass $=0.38 \mathrm{kg},$ radius $=0.028 \mathrm{m}$ ) may each be treated as uniform spheres. What is the magnitude of the maximum gravitational force that each can exert on the other?

Answer

$9.6 \times 10^{-9} N$

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Video Transcript

This is the bowling ball and disease. The billiard ball, too. When is the magnitude of the gravitational force that one exert all the other one is maximum? Well knows the following the equation that he was. The magnitude of the reputation of attraction between these two bowls is the following. F G is equal to the noodles, constant times the mass off the bowling ball times the mass off the billiard ball divided by the distance between the their centers squared. So as the distance between their centers begun becomes smaller. So as we decrease r squared, we are increasing the force. So the situation when this force is the maximum possible is well, they are US clues as possible, which is this one. So this is the situation when the gravitational attraction between both of these balls is the maximum and in the situation, what is the distance between their centers? Well, note that these is the radio's off the bowling ball, and these is the radios off the billiard boat, so the distance between their centers is equals. Two. This some off the radios off this both off both of these two bowls, then the magnitude after reputation. Attraction between them is given by neuters constant G, which, if you forgot, is equal to 6.67 times. Stand to minus 11 new tones. Meters squared, divided by kilograms squared so 6.67 times stand. The line is 11 times the mass off the bowling ball, 7.2 kilograms stands the mask off the billiard boat, 0.38 kilograms, divided by the distance between their centers squared, which is 0.11 plus 0.0 28 squared. And this gives us a gravitational force off approximately 9.6 times, then to minus nine do teams. So this is the maximum gravitational force one Balkan dessert on the other one. So it is a very, very, very small force almost imperceptible for us.