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A block of mass m is attached with a massless spring of force constant K. the block is placed over a rough inclined surface for which the coefficient of friction is `mu =3/4` find the minimum value of M required to move the block up the place. (Neglect mass of string and pulley. Ignore friction in pulley). .A. (a) `3/5m`B. (b) `4/5m`C. (c) `6/5m`D. (d) `3/2m` |
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Answer» Correct Answer - C As long as the block of mass m remains staionary, the block of mass M released from rest let it comes down by distance x, applying conservation of mechanical energy `DeltaK+DeltaU=0implies0+(DeltaU_(gravity)+DeltaU_(spri ng))=0` `(-Mgx+1/2kx^2)=0impliesx=(2Mg)/(k)` Thus at the maximum extension in spring is `kx=2Mg` ...(1) For block of mass m to just move up the incline `kx=mg sin theta+mu mg cos theta` ...(2) `2Mg=mgxx3/5+3/4mgxx4/5` or `M=3/5m` |
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