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Physics Part I

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Physics

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Class 10 Class 12

Two similar springs P and Q have spring constants KP and KQ, such that KP>KQ. They are stretched, first by the same amount (case a), then by the same force (case b). The work done by the springs WP and WQ are related as, in  case (a) and case (b), respectively

  • WP =WQ ;WP> WQ

  • WP =WQ ;WP= WQ

  • WP > WQ ;WQ> WP

  • WP <WQ ; WP< WQ


C.

WP > WQ ;WQ> WP

Given KP>KQ
In case (a) the elongation is same
straight x subscript 1 space equals space straight x subscript 2 space equals straight x
straight W subscript straight P space equals space 1 half straight K subscript straight P straight x squared
and space space straight W subscript straight Q space equals space 1 half straight K subscript straight Q straight x squared
therefore space fraction numerator straight W subscript straight P over denominator straight W subscript straight Q space end fraction space equals space straight K subscript straight P over straight K subscript straight Q greater than 1
rightwards double arrow space straight W subscript straight P greater than straight W subscript straight Q
In space case space left parenthesis straight b right parenthesis space the space spring space force space is space same
straight i. straight e space straight F subscript 1 space equals space straight F subscript 2 equals straight F
straight x subscript 1 equals straight F over straight K subscript straight P comma space straight x subscript 2 space equals space straight F over straight K subscript straight Q
therefore space straight W subscript straight P space equals space 1 half straight K subscript straight P straight x subscript 1 superscript 2 space equals space 1 half straight K subscript straight P space fraction numerator straight F squared over denominator straight K subscript straight P superscript 2 end fraction space equals space 1 half straight F squared over straight K subscript straight P
and space space straight W subscript straight Q space equals space 1 half straight K subscript straight Q straight x subscript 2 superscript 2 space equals space 1 half straight K subscript straight Q space fraction numerator straight F squared over denominator straight K subscript straight Q superscript 2 end fraction space equals space 1 half straight F squared over straight K subscript straight Q
straight W subscript straight P over straight W subscript straight Q equals space straight K subscript straight Q over straight K subscript straight P space less than 1
straight W subscript straight P space less than space straight W subscript straight Q
 

Given KP>KQ
In case (a) the elongation is same
straight x subscript 1 space equals space straight x subscript 2 space equals straight x
straight W subscript straight P space equals space 1 half straight K subscript straight P straight x squared
and space space straight W subscript straight Q space equals space 1 half straight K subscript straight Q straight x squared
therefore space fraction numerator straight W subscript straight P over denominator straight W subscript straight Q space end fraction space equals space straight K subscript straight P over straight K subscript straight Q greater than 1
rightwards double arrow space straight W subscript straight P greater than straight W subscript straight Q
In space case space left parenthesis straight b right parenthesis space the space spring space force space is space same
straight i. straight e space straight F subscript 1 space equals space straight F subscript 2 equals straight F
straight x subscript 1 equals straight F over straight K subscript straight P comma space straight x subscript 2 space equals space straight F over straight K subscript straight Q
therefore space straight W subscript straight P space equals space 1 half straight K subscript straight P straight x subscript 1 superscript 2 space equals space 1 half straight K subscript straight P space fraction numerator straight F squared over denominator straight K subscript straight P superscript 2 end fraction space equals space 1 half straight F squared over straight K subscript straight P
and space space straight W subscript straight Q space equals space 1 half straight K subscript straight Q straight x subscript 2 superscript 2 space equals space 1 half straight K subscript straight Q space fraction numerator straight F squared over denominator straight K subscript straight Q superscript 2 end fraction space equals space 1 half straight F squared over straight K subscript straight Q
straight W subscript straight P over straight W subscript straight Q equals space straight K subscript straight Q over straight K subscript straight P space less than 1
straight W subscript straight P space less than space straight W subscript straight Q
 

2555 Views

Define the unit joule.

Work done is said to be one joule if one newton of  force displaces the body through a distance of one meter in the direction of applied  force .
799 Views

Is work a scalar or a vector quantity?

Work is dot product of two vectors. i.e. F with rightwards arrow on top times S with rightwards arrow on top.

And dot product is a scalar quantity. Therefore, work is a scalar quantity. 
1450 Views

What are different units of energy?

The different units of energy are :

(i) Joule            
(ii) Erg
(iii) eV            
(iv) KWh
(v) Calorie.

804 Views

What is watt?

SI unit of power is Watt. 
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Define watt.

Power is said to be one watt if one joule of work is done in one second. 
860 Views

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