Laws Of Motion Question 396
Question: 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.)
Options:
A) $ \frac{3}{5}m $
B) $ \frac{4}{5}m $
C) $ \frac{6}{5}m $
D) $ \frac{3}{2}m $
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Answer:
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 $
