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two ice skaters, paul and tom, are each holding on to opposite ends of the same rope. each pulls the other toward him. the magnitude of paul's acceleration is 1.25 times greater than the magnitude of tom's acceleration. what is the ratio of paul's mass to tom's mass? (a) 0.67 (b) 0.80 (c) 0.25 (d) 1.25 (e) 0.50



Answer :

If the magnitude of Paul's acceleration is 1.25 times greater than  Tom's acceleration , then the ratio of Paul's mass to Tom's mass is  0.80  .

There are two Ice skaters , Paul and Tom ;

they are holding the opposite ends of the same rope ;

and also given that magnitude of Paul's acceleration is 1.25 times greater than  Tom's acceleration ;

we know that by Newton's second Law ⇒ F = ma ;

So , the ratio can be written as :

(Paul's mass)/(Tom's mass) = (Tom's acceleration)/(Paul's acceleration)

Substituting the values ,

we get ;

(Paul's mass)/(Tom's mass) = 1/1.25

= 0.80  .

Therefore , the ratio of Paul's mass to Tom's mass is 0.80   .

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