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 $\mu =3/4$. 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. $2m$
• D. $\frac{3}{2}m$

Answer 1

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

Let mass $M$ decends $x$ meter to lift the load then

$kx=mg\sin \theta +\mu mg\cos \theta$

$kx=6m+6m$

$kx=12m$

Now,

Applying work energy theorm,

$W_{spring}+W_{gravity}=$change in K.E

$-\frac{1}{2}k{x}^2+Mgx=0$

$kx=2Mg$

$12m=2Mg$

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

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