Question

A block of mass $m$ is attached with a massless spring of force constant $k$. The block is placed over a rough incline surface for which the coefficent of frictionless is$\mu =3/4$. The minimum value of $M$ required to move the block up the plane is then (Neglect mass of string and pulley and friction in pulley)

• A. $6/5m$
• B. $4/5m$
• C. $2m$
• D. $3/2m$

Answer 1

The correct option is A $6/5m$

Given that,

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

Now, according to figure

Force on block of mass $M$ – tension $T$ and $Mg$ downward

Now, block is placed over inclined it is in rest

So, $T=mg$

Now,

$T=mg\sin {37}^0+\mu mg\cos {37}^0$

$M=m(\frac{3}{5}+\frac{3}{4}\times \frac{4}{5})$

$M=\frac{6m}{5}$

Hence, the mass is $\frac{6m}{5}$