# 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

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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