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Question

A moon of mass $m$ orbits a planet of mass 100 $\mathrm{m}$ . Let the strength of the gravitational force exerted by the planet on the moon be denoted by $F_{1},$ and let the strength of the gravitational force exerted by the moon on the planet be $F_{2} .$ Which of the following is true?
(A) $F_{1}=10 \mathrm{OF}_{2}$
(B) $F_{1}=1 \mathrm{O} F_{2}$
(C) $F_{1}=F_{2}$
(D) $F_{2}=10 F_{1}$

Vipender Yadav · Accepted Answer

so here in this problem were given that the moon off moss m orbits a planet off mass 100 m So the mass off moon were given as M on the mosque off planet were given us 100 m on F one day. Not the strength off the gravitation force off force exerted by the planet on the moon on the force If tow, it denotes the strength of gravitation force exerted by the moon on the planet and therefore options given on we have to tell that which option is correct. Now we know that the gravitational force is given by if is equals toe g m one m two divide by our square. So if we calculate f one, it should be called stogie. Everyone here is m that the mouse off moon m to Harris 100 him divide by our square so it will be equals two g m squared times 100 So 100 I&#x27;m writing here divide by our square Now next if we calculate the value of F two will be using the same formula. If there will be calls to G here and one will become 100 him times Mt will become him divide by are square. They are represents the distance between the two bodies. So if you see both the expressions we find that everyone is equal to F two. So we can say that option C is correct. See? Option is correct. So I hope you have understood the problem. Thank you.

Ze-Han Lee · Answer

So in this problem we have a moon and we have a planet. So the gravitational force exerted by the planet on the morning is F one and the gravitational pull is accepted by F by the morning on the planet is up to. So these two forces the ex reformed action and reaction force. So f one F two, they have the same magnitude but to their opposite.

Ankit Gupta · Answer

According to Newton&#x27;s Law of Gravitation, the force of attraction between two objects has given us G multiplied with M one m two divided by r squared very modern him two of the mass of the two objects Jeez, universal gravitation, constant and RSD distance between the centres off these two bodies. So let&#x27;s speak X as the distance from the earth. Very the force off attraction Due to the moon, it will be greater than the force off attraction due to the earth. Now we need to find X such that force off attraction doodle The moon at this distance will be greater than force of attraction due to the earth at this distance. So we can say that we need to find the force of attraction due to moon divided by the force of attraction due to ought at this distance should be greater than one. So putting the values according to the formula for the force of attraction. As per Newton, we&#x27;ll get G multiplied wit m where m is the moss off the body m m being the moss off moon divided by R minus X squared, divided by G. M m E, where m is the mass off the earth divided by X squares should be greater than one. So then g, m and G m will get cancelled because they&#x27;re the same. So the inequality of allow change toe m m multiplied with X squared is greater than M E multiplied with ar minus. X holds Quit. Now let&#x27;s all photo Now if we take away mm X squared from both sides so the inequality will become M M X squared minus M m X Trail is greater than M E R Square plus M E X squared minus twice off m E multiplied with ar minus X minus M m X square. So now cancelling out and rearranging, we are going to get the final inequality as zero is greater than M E multiplied with R squared minus to our X plus X squared minus m m exquisite, which will become Mars offered. Miners mass off moon multiplied with X squared minus two are must off Earth multiplied. Videx plus R squared multiplied with Marceau Effort is less than zero now, putting the values form us off earth mass off Moon on the radius. We&#x27;re going to get 5.9742 multiplied with 10 to the power of 24 miners, 7.349 multiplied with 10 to the power off 20 to minus two multiplied with 384,400 multiplied with 5.9742 multiplied with tend to the part of 24 plus 384,000 and 400 squared multiplied with five point 9749 into 10. Raise to the part of 24 will be less than zero, which will give us on solving that X should lie between one point through seven multiplied with 10 days to the bar seven on day zero. So therefore the solution said will be zero on 1.27 into 10 race to the par off seven kilometers.

James Leslie · Answer

the museum&#x27;s law says that Force F is equal to G terms and one times end to all over D squared. Margie is the gravitational constant, and one of them to the masses and d is distance between two objects. So okay, so right. The first question is you want to find, um d f by the d o. I guess work better the rate of change of force, respect distance when g. M London and pure Constance The second question that sends to find this oh, evaluated with the given information. So let&#x27;s go ahead. And so the problem. So one now all way g m one into your conscience. So we can write this as f equals G and one and two times, huh? That one over the squared And this terror of the front is just constant. So this implies that the F by the hey is equal to well, this time here, this is just beach minus two. So they dropped him of This is just going to be minus two D to my three. So this implies that our overall derivative is going to be lions, too. G m one and two. Well, the D Q. So that&#x27;s the first part down. That&#x27;s the drifted there. The second part is to evaluate this with the given information on dhe. So this distance D should be 1000. What? This is 10. Keep it. Okay. Right. So let&#x27;s that&#x27;s a look and see if we can get so we want, uh, input this these bits of data in red into that derivative. So we&#x27;ve got minus two times 6.67 times 10 to the minus 11 and then and one and two. Sorry. What am I doing? This here? This is a 10 and the mess. Thank you. It&#x27;s not like it. So right. And one and two. So that&#x27;s going to be times 10 cute times 10. Cute. Pull over. Now it&#x27;s the cute. So this could be a liver and cute. So you just can&#x27;t sell one of these out, and I&#x27;m definitely left with minus two times 6.67 times 10 MLD powers of 10. That&#x27;s gonna have the three times 10 to the minus eight. And this is their our answer on Just add at the end. So because this is essentially a question phrased in terms of physics. We have units on dhe. The units of this because we&#x27;re dealing with change of force were expected. Change in distance. Could be new tins. Meter. There are those, even it. And if we really wanted to, we could simplify. Or we could multiply these numbers out together, and we&#x27;d have something like 1.334 or something like that. Times 10 to the minus seven. This is his plan for me.

Brandi Roebuck · Answer

The equation of gravitational force is equal to the dis. The mass of the first object multiplied by the mass of the second objects divided by the distance between the two objects well supplied by G, which is the, uh, which is the universal gravitational constant. So this is the equation were given to work with, and then we&#x27;re given two masses and a distance. So our force, their gravitational force, is going to be equal to the mass of Earth most applied by the mass of the moon divided by the distance between those two bodies, the mass of Earth is five 0.97 times 10 to the 20 four multiplied by. I&#x27;m actually gonna change up the notation here to save a little bit of space. So instead of doing times 10 I&#x27;m actually gonna do E 24 multiplied by seven point three. They were gonna make it even easier to see 7.36 Eves when it&#x27;s too divided by 3.84 Yeah, aches well supplied by she. I&#x27;m not gonna re I&#x27;m not gonna rewrite G over there for the sake of space, but we see the G is equal to 6.67 e negative 11. So when we throw this in a calculator, we&#x27;re going to get some that is very close to two times 10 to the 20th. It&#x27;s actually 1.99 times 10 to the 20th. So there&#x27;s your answer. Thanks for tuning in.

Zulfiqar Ali · Answer

Let&#x27;s to part in in Barkey Recalculate cracked ation force exerted by sun on moon. So cramp additional force Gravitational force exerted, uh, exerted by sun on moon by son on more right. So let&#x27;s make the following assumptions Number one Since the moon orbits the earth, it is reasonable to use the radial distance between the sun and the earth in the calculation. So radial distance, uh, radio distance between the sun between the sun and the birth and the earth in the calculation in the calculation. Right. And number two, well, as in the orbital beaded off the moon around the sun is also the same is arts so azeem on the on beat old Let&#x27;s die right down t for the on between period so t off the moon around the sun The moon around the sun is also the same. It&#x27;s also the same is art right? Okay. Now, um, let&#x27;s calculate the radial distance Well regular distance R is given by key brute off uh g times, Marcel son Times D square, divided by for by square and by substituting values we have Route three into GLG is 6.67 times 10 to the power minus 11. Right multiply by Marcel Sonny&#x27;s two times 10 to the Power 30. And then we have the orbital pdf that&#x27;s converting two seconds. 65 multiplied by 24 multiplied by 3600. Whole square, right, divided by for by square for by spare. So our is he cool, too. 1.5. Multiply by 10 to the power 11 meter. Okay, now let&#x27;s find out the gravitational force exerted by sun on moon. For bait, we apply loaf Universal gravitation. So four So son on moon is equal to G times, which is a crab station. X relation muscle Sun Times Marcel&#x27;s Moon divided by R Square so buying substituting Values 6.67 Multiply by 10 to the power minus 11 uh, times to multiply by 10 to the power 30 multiplied by 7.35 Multiply by 10 to the power 22 Divided by R Square, which is 1.5. Multiply by 10 to the power 11 whole square. Therefore, the force exerted by sun on monies for find 36 multiply by tend to depart 20 Newton right and now let&#x27;s calculate force exerted by Arto Moon so the force exerted by our Thorman Ford&#x27;s exerted by earth on moon is equal to G times months off. Earth times Marcel Moon divided by hard square. Well, here, um, I substituting values six point 67 multiply by 10 to the power minus 11. Marceau 46 times 10 to the power 24 and moss off Mooney&#x27;s 7.35 months of life. I tend to the power 22 divided by are square Well, our is 3.8 motive live. I tend to the power he told square do for gravitational force exerted by Arthur own moon is equal to do 0.4 multiply by 10 to the power 20 uh, Newton. No. Uh so this waas uh, the keys, uh, force exerted by art on the mornings 2.4 multiplied temporary power 20 Newtons from the universal law of gravitation of his Newton&#x27;s third Law Therefore, force, um exerted by art on morn is equal to force exerted by moon on earth and the magnitude of forces equals 2.4 Multiply by 10 to the power 20 Newton

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