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Mechanical Properties Of Fluids

Question
CBSEENPH11020781

A vertical spring with force constant k is fixed on a table. A ball of mass m at a height h above the free upper end of the spring falls vertically in the spring. so that the spring is compressed by a distance d. The net work done in the process is:

  • mg space left parenthesis straight h plus straight d right parenthesis space space plus space 1 half space kd squared
  • mg space left parenthesis straight h plus straight d right parenthesis space space minus space 1 half space kd squared
  • mg space left parenthesis straight h minus straight d right parenthesis space space minus space 1 half space kd squared
  • mg space left parenthesis straight h minus straight d right parenthesis space space plus space 1 half space kd squared

Solution

B.

mg space left parenthesis straight h plus straight d right parenthesis space space minus space 1 half space kd squared

Work done is equal to change in energy of the body.
The situation is shown in the figure. When mass m falls vertically on spring, then spring si compressed by distance d.

Hence, network done in the process is 
W= Potential energy stored in the spring + Loss of potential energy of mass 

mg space left parenthesis straight h plus straight d right parenthesis space space minus space 1 half space kd squared