  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. μ1 and μ2 are the coefficients of friction between the blocks as shown. Column I gives the different relations between μ1 and μ2, and Column II is regarding the motion of M. Match the columns Column IColumn IIi.If μ1=μ2=0a.May accelerate towards rightii.If μ1=μ2≠0b.May accelerate towards leftiii.If μ1>μ2c.Does not accelerateiv.If μ1<μ2d.May or may not acceleratei - c;  ii - c; iii - b,d; iv - ai - c;  ii - c; iii - b,d; iv - a,di - c;  ii - c; iii - b; iv - a,di - c;  ii - d, iii - b,d; iv - a,d

Solution

## The correct option is B i - c;  ii - c; iii - b,d; iv - a,d(i) If μ1=μ2  = 0, then there is no force on M in horizontal direction. So M does not accelerate. Hence (i) - (c) (ii) If μ1=μ2 ≠ 0 f1 and f2 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) μ1>μ2, here f1 > f2 when the blocks slides, and f1 = f2 when the blocks does not slide. Hence, (iii) - (b), (d) (iv) μ1<μ2, here f1 < f2 when the blocks slides, and f1 = f2 when the blocks does not slide. Hence, (iv) - (a), (d)  Suggest corrections   