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Q. Statement 1: If the work done by force other than conservative forces is zero, then mechanical energy is conserved.
Statement 2: The work done by non-conservative forces is always negative.

Work, Energy and Power

Solution:

Statement-1 is true, Statement-2 is false.
$W_{\text {other }}=\Delta K+\Delta U$
If $W_{\text {other }}=0,$ then $\Delta K+\Delta U=0$. If a block is sitting over another block. Suppose the lower block is moved and the upper block moves along. Then work is done by static friction on the upper block and it is +ve.