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Easy

Question

External forces acting on a rod of length L, cross-sectional area A and Young's modulus Y are as shown in the figure. Choose the correct alternative

  1. there will be a change in length only in parts 2 and 3
  2. no change in length of rod is observed
  3. the net elongation of the whole rod is fraction numerator F L over denominator 2 A Y end fraction
  4. the net compression of the whole rod is fraction numerator F L over denominator A Y end fraction

The correct answer is: the net elongation of the whole rod is fraction numerator F L over denominator 2 A Y end fraction


    Net elongation equals fraction numerator F L over denominator A Y end fraction minus fraction numerator F left parenthesis L divided by 2 right parenthesis over denominator A Y end fraction equals fraction numerator F L over denominator 2 A Y end fraction

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    A t space 40 to the power of 0 space C comma space a space b r a s s space w i r e space o f space 1 space m m space r a d i u s space i s space h u n g space f r o m space t h e space c e i l i n g. space A space s m a l l space m a s s comma space M space i s space h u n g space f r o m space t h e space f r e e space e n d space
o f space t h e space w i r e. space W h e n space t h e space w i r e space i s space c o o l e d space d o w n space f r o m space 40 to the power of 0 C space t o space 20 to the power of 0 C space i t space r e g a i n s space i t s space o r i g i n a l space l e n g t h space o f space 0.2 space m. space T h e space
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d e p r e s s e d space b y space a n space a m o u n t space h space i n space a space c a p i l l a r y space t u b e space o f space r a d i u s space r subscript 1 comma space w h i l e space w a t e r space r i s e s space b y space t h e space s a m e space a m o u n t space h space i n space a space
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w i r e s space s t r e t c h space b y space t h e space s a m e space l e n g t h space f o r space a space g i v e n space l o a d comma space t h e n space t h e space v a l u e space o f space R space i s space c l o s e space t o

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w h a t space w i l l space b e space t h e space t e n s i l e space s t r e s s space t h a t space w o u l d space b e space d e v e l o p e d space i n space t h e space w i r e ?

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w h a t space w i l l space b e space t h e space t e n s i l e space s t r e s s space t h a t space w o u l d space b e space d e v e l o p e d space i n space t h e space w i r e ?

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T h e space b o y space k e e p s space a space s t o n e space w e i g h i n g space 0.02 space k g space o n space i t space a n d space s t r e t c h e s space t h e space c o r d space b y space 20 space c m space b y space a p p l y i n g space a space c o n s tan t space f o r c e. space W h e n space r e l e a s e d comma space
t h e space s t o n e space f l i e s space o f f space w i t h space a space v e l o c i t y space o f space 20 space m s to the power of negative 1 end exponent. space N e g l e c t space t h e space c h a n g e space i n space t h e space a r e a space o f space c r o s s minus s e c t i o n space o f space t h e space c o r d space w h i l e space s t r e t c h e d. space
T h e space Y o u n g ’ s space m o d u l u s space o f space r u b b e r space i s space c l o s e s t space t o space minus space

    A space b o y ’ s space c a t a p u l t space i s space m a d e space o f space r u b b e r space c o r d space w h i c h space i s space 42 space c m space l o n g comma space w i t h space 6 space m m space d i a m e t e r space o f space c r o s s minus s e c t i o n space a n d space o f space n e g l i g i b l e space space m a s s. space
T h e space b o y space k e e p s space a space s t o n e space w e i g h i n g space 0.02 space k g space o n space i t space a n d space s t r e t c h e s space t h e space c o r d space b y space 20 space c m space b y space a p p l y i n g space a space c o n s tan t space f o r c e. space W h e n space r e l e a s e d comma space
t h e space s t o n e space f l i e s space o f f space w i t h space a space v e l o c i t y space o f space 20 space m s to the power of negative 1 end exponent. space N e g l e c t space t h e space c h a n g e space i n space t h e space a r e a space o f space c r o s s minus s e c t i o n space o f space t h e space c o r d space w h i l e space s t r e t c h e d. space
T h e space Y o u n g ’ s space m o d u l u s space o f space r u b b e r space i s space c l o s e s t space t o space minus space

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    W a t e r space f r o m space a space p i p e space i s space c o m i n g space a t space a space r a t e space o f space 100 space l i t e r s space p e r space m i n u t e. space I f space t h e space r a d i u s space o f space
t h e space p i p e space i s space 5 space c m comma space t h e space R e y n o l d s space n u m b e r space f o r space t h e space f l o w space i s space o f space t h e space o r d e r space o f space minus space
left parenthesis d e n s i t y space o f space w a t e r space equals space 1000 space k g divided by m cubed comma space c o e f f i c i e n t space o f space v i s cos i t y space o f space w a t e r space equals space 1 space m P a space s right parenthesis space

    W a t e r space f r o m space a space p i p e space i s space c o m i n g space a t space a space r a t e space o f space 100 space l i t e r s space p e r space m i n u t e. space I f space t h e space r a d i u s space o f space
t h e space p i p e space i s space 5 space c m comma space t h e space R e y n o l d s space n u m b e r space f o r space t h e space f l o w space i s space o f space t h e space o r d e r space o f space minus space
left parenthesis d e n s i t y space o f space w a t e r space equals space 1000 space k g divided by m cubed comma space c o e f f i c i e n t space o f space v i s cos i t y space o f space w a t e r space equals space 1 space m P a space s right parenthesis space

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