Question

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 $\mu =\frac{3}{4}.$ Find the minimum value of M required to move the block up the plane. (Neglect mass of string and pulley. Ignore friction in pulley).

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

Answer 1

The correct option is D $\frac{6}{5}m$

When the block of mass $M$ tends to move block of mass $m$ upwards, the gravitational force downward along the incline and frictional force downwards along the incline just get balanced by the tension in the string.

Thus $T=mgsin{37}^{\circ }+\mu mgcos{37}^{\circ }$

$⟹Mg=mg\frac{3}{5}+\frac{3}{4}mg\frac{4}{5}$
$⟹M=\frac{6}{5}m$