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

  • Option 1)

    mg(h + d) - (1/2)kd2 
     

  • Option 2)

    mg(h - d) - (1/2)kd2 

  • Option 3)

    mg(h - d) + (1/2)kd2 
     

  • Option 4)

    mg(h + d) (1/2)kd2
     

 

Answers (1)

As we discussed in concept

If only conservative forces act on a system, total mechnical energy remains constant -

K+U=E\left ( constant \right )

\Delta K+\Delta U=0

\Delta K=-\Delta U

-

 

 W=mg(h+d)-\frac{1}{2}kd^{2}


Option 1)

mg(h + d) - (1/2)kd2 
 

Option is correct

Option 2)

mg(h - d) - (1/2)kd2 

Option is incorrect

Option 3)

mg(h - d) + (1/2)kd2 
 

Option is incorrect

Option 4)

mg(h + d) (1/2)kd2
 

Option is incorrect

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