GRAVITATION. 49 



EXERCISES. 



1. How far below the surface of the earth will a ten-pound ball 

 weigh only four pounds ? 



Solution. 



Formula: w : W :: d : D. 



Substituting ; 4 : 10 : : d : 4000 

 lQd= 16000 



d=1600 miles from centre. 

 40001600=2400 miles below the surface. Ans. 



2. What would a body weighing 550 Ibs. on the surface of the 

 earth weigh 3,000 miles below the surface ? Ans. 137 Ibs. 



3. Two bodies attract each other with a certain force when they 

 are 75 m. apart. How many times will the attraction be increased 

 when they are 50 m. apart ? Ans. 2\. 



4. Given three balls. The first weighs 6 Ibs. and is 25 ft. distant 

 from the third. The second weighs 9 Ibs. and is 50 ft. distant from 

 the third, (a) Which exerts the greater force upon the third? 

 (&) How many times greater ? Ans. f . 



5. A body at the earth's surface weighs 900 pounds ; what would 

 it weigh 8,000 miles above the surface ? 



6. How far above the surface of the earth will a pound avoirdupois 

 weigh only an ounce? 



7. At a height of 3,000 miles above the surface of the earth, 

 what would be the difference in the weights of a man weighing 200 

 Ibs. and of a boy weighing 100 Ibs. ? 



8. Find the weight of a 180 Ib. ball (a) 2,000 miles above the 

 earth's surface ; (6) 2,000 miles below the surface. 



9. (a) Would a 50 Ib. cannon ball weigh more 1,000 miles above 

 the earth's surface, or 1,000 miles below it ? (&) How much ? 



10. If the moon were moved to three times its present distance 

 from the earth, what would be the effect (a) on its attraction for 

 the earth ? (6) On the earth's attraction for it ? 



11. How far below the surface of the earth must an avoirdupois 

 pound weight be placed in order to weigh one ounce ? 



12. How far above the surface of the earth must 2,700 pounds be 

 placed to weigh 1,200 pounds ? Ans. 2,000 miles. 



107. Centre of Gravity. The centre of grav- 

 ity of a body is the point about which all the 

 matter composing the body may be balanced. 

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