| A block of mass m is attached with massless spring of force constant k. The block is placed over a fixed rough inclined surface for which the coefficient of friction is \[\mu =3/4.\] The block of mass m is initially at rest. The block of mass M is released from rest with spring in unstretched state. The minimum value of M required to move the block up the plane is (neglect mass of string and pulley and friction in pulley.) |
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A) \[\frac{3}{5}m\]
B) \[\frac{4}{5}m\]
C) \[\frac{6}{5}m\]
D) \[\frac{3}{2}m\]
Correct Answer: A
Solution :
| As long as the block of mass m remains stationary, the block of mass M released from rest comes down by \[\frac{2Mg}{K}\] (before coming it rest momentarily again). Thus the maximum extension in the spring is \[x=\frac{2Mg}{K}\] ...(1) |
| For block of mass m to just move up the incline \[kx=mg\sin \theta +\mu \,mg\cos \theta \] .....(2) |
| \[2Mg=mg\times \frac{3}{5}+\frac{3}{4}mg\times \frac{4}{5}\] or \[M=\frac{3}{5}m\] |
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