Question

For the figure, both the pulleys are massless and frictionless. The right side pully can move. A force F, of any possible magnitude, is applied in horizontal direction. There is no friction between M and ground.
${\mu }_{1}and{\mu }_2$ are the coefficients of friction between the blocks as shown. Column I gives the different relations between ${\mu }_{1}and{\mu }_2$,and Column II is regarding the motion of M. Match the columns


$\begin{array}{cccc}& \text{Column I}& & \text{Column II}\\ \text{i.}& \text{If}\mu 1=\mu 2=0& \text{a.}& \text{May accelerate towards right}\\ \text{ii.}& \text{If}\mu 1=\mu 2\ne 0& \text{b.}& \text{May accelerate towards left}\\ \text{iii.}& \text{If}\mu 1>\mu 2& \text{c.}& \text{Does not accelerate}\\ \text{iv.}& \text{If}\mu 1<\mu 2& \text{d.}& \text{May or may not accelerate}\end{array}$

• A. i - c; ii - c; iii - b,d; iv - a
• B. i - c; ii - c; iii - b,d; iv - a,d
• C. i - c; ii - c; iii - b; iv - a,d
• D. i - c; ii - d, iii - b,d; iv - a,d

Answer 1

The correct option is B i - c; ii - c; iii - b,d; iv - a,d

(i) If ${\mu }_1={\mu }_2$$=0$, then there is no force on M in horizontal direction.
So M does not accelerate.
Hence (i) - (c)

(ii) If ${\mu }_1={\mu }_2$$\ne 0$
$f_{1}and{f}_2$ will be of the same magnitude at any time whether the blocks slip on larger block or not, so net force on M is zero. Hence, M does not accelerate. So (ii) - (c)
(iii) ${\mu }_1>{\mu }_2$, here f1 > f2 when the blocks slides, and f1 = f2 when the blocks does not slide.
Hence, (iii) - (b), (d)
(iv) ${\mu }_1<{\mu }_2$, here f1 < f2 when the blocks slides, and f1 = f2 when the blocks does not slide.
Hence, (iv) - (a), (d)