Question

A block of mass ${}^{\prime }{m}^{\prime }$ is attached with a massless spring of force constant $k$. The block is placed over a rough incline surface for which the coefficient of friction is $\mu =\frac{3}{4}$. The minimum value of $M$ required to moved the block up the plane is (Neglect mass of pulley, string 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 $\frac{3}{5}m$

Given,

Coefficient of friction, $\mu =\frac{3}{4}$

Mass of block A is $M$

Mass of block B is $m$

When block A moves to a distance $x$, then spring will stretch to $x$ value. And it will lift the block B

For, block B and spring

Maximum Force required on spring = gravity force component + friction force

Force in the spring, $F=kx=mg\sin {37}^o+\mu mg\cos {37}^o$

$\Rightarrow kx=mg\frac{3}{5}+\frac{3}{4}mg\frac{4}{5}=\frac{6mg}{5}\dots \dots \left(1\right)$

For, block A and spring

Kinetic energy = Potential energy

$\frac{1}{2}k{x}^2=Mgx$

$kx=2Mg......\left(2\right)$

From (1) and (2)

$\frac{6mg}{5}=2Mg$

$M=\frac{3m}{5}$

Required mass of A is $\frac{3m}{5}$ , to lift mass B