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 $\mu =\frac{3}{4}.$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.)

• A. $\frac{3}{5}m$
• B. $\frac{4}{5}m$
• C. $\frac{6}{5}m$
• D. $\frac{3}{2}m$

Answer 1

The correct option is A $\frac{3}{5}m$

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 $kx=mgsin\theta +\mu mgcos\theta$........(2)