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CBSE Class 9 Answered

two objects of mass m1 and m2 when separated by distance 'd' in air attract each other.with a force of 4N how is the magnitude of force changed when masses of both objects are reduced to one half???
Asked by arajeevshashank | 28 Aug, 2019, 06:30: PM
answered-by-expert Expert Answer
The gravitational force is given as, 
 
F space equals fraction numerator G m subscript 1 m subscript 2 over denominator d squared end fraction
W h e n space t h e space d i s tan c e space i s space d space t h e space f o r c e space i s space 4 N space
T h u s comma space
4 space equals space fraction numerator G m subscript 1 m subscript 2 over denominator d squared end fraction space... left parenthesis 1 right parenthesis

W h e n space t h e space m a s s space o f space b o t h space b o d i e s space a r e space r e d u c e d space t o space h a l f space t h e n comma space
F apostrophe space equals fraction numerator G open parentheses begin display style m subscript 1 over 2 end style close parentheses open parentheses begin display style m subscript 2 over 2 end style close parentheses over denominator d squared end fraction... left parenthesis 2 right parenthesis
T a k i n g space r a t i o s space o f space 1 right parenthesis space a n d space 2 right parenthesis
fraction numerator F over denominator F apostrophe end fraction equals fraction numerator fraction numerator G m subscript 1 m subscript 2 over denominator d squared end fraction over denominator fraction numerator G open parentheses begin display style m subscript 1 over 2 end style close parentheses open parentheses begin display style m subscript 2 over 2 end style close parentheses over denominator d squared end fraction end fraction space equals space 4 over 1

T h u s comma

fraction numerator 4 over denominator F apostrophe end fraction equals 4 over 1
T h u s comma space
F apostrophe space equals space 1 space N space left parenthesis w h e n space t h e space m a s s e s space a r e space r e d u c e d space t o space h a l f right parenthesis space
 
 
Thus, when masses are reduced to half the magnitude of the force is reduced to the one-fourth of the initial value. 
Answered by Utkarsh Lokhande | 29 Aug, 2019, 08:26: AM
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