1. When an elastic material with Young’s modulus Y is subjected to stretching stress S, elastic energy stored per unit volume of the material is

1. 1. YS/2

   
   
   

   2. S²Y/2

   
   
   

   3. S²/2Y

   
   
   

   4. S/2Y

   
   
   

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1. View Hint View Answer Discuss in Forum

   Energy stored per unit volume =
   

   =	1	× stress × strain
   	2

   
   

   =	1	× stress × (stress/ Young's modulus)
   	2

   
   

   =	1	× stress²/ (Young's modulus)
   	2

   
   

   =	S²	× stress²/ (Young's modulus)
   	2Y

   
   

   Correct Option: C

   Energy stored per unit volume =
   

   =	1	× stress × strain
   	2

   
   

   =	1	× stress × (stress/ Young's modulus)
   	2

   
   

   =	1	× stress²/ (Young's modulus)
   	2

   
   

   =	S²	× stress²/ (Young's modulus)
   	2Y

   
   

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2. The bulk modulus of a spherical object is 'B'. If it is subjected to uniform pressure 'p', the fractional decrease in radius is

1. 1. B

      3p

   
   
   

   2. 3p

      B

   
   
   

   3. p

      3B

   
   
   

   4. p

      B

   
   
   

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1. View Hint View Answer Discuss in Forum

   Bulk modulus is given by
   

   B =	P
   		AV
   		V

   
   

   Or	ΔV	=	P
   	V		B

   
   

   3	ΔR	=	P
   	R		B

   
   (here, = ΔR/R fractional decreases in radius)
   

   ⇒	ΔR	=	P
   	R		3B

   Correct Option: C

   Bulk modulus is given by
   

   B =	P
   		AV
   		V

   
   

   Or	ΔV	=	P
   	V		B

   
   

   3	ΔR	=	P
   	R		B

   
   (here, = ΔR/R fractional decreases in radius)
   

   ⇒	ΔR	=	P
   	R		3B

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