The figure shows a two-block system. $A$ $4 \,kg$ block rests on a smooth horizontal surface,and the upper surface of the $4 \,kg$ block is rough. $A$ block of mass $2 \,kg$ is placed on its upper surface. Given $\mu_s = 0.8$ and $\mu_k = 0.6$ between the two blocks. The acceleration of the upper block with respect to the earth when the $4 \,kg$ mass is pulled by a force of $30 \,N$ is ......... $m/s^2$.

  • A
    $6$
  • B
    $5$
  • C
    $8$
  • D
    $2$

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$A$ $40 \,kg$ slab rests on a frictionless floor as shown in the figure. $A$ $10 \,kg$ block rests on the top of the slab. The static coefficient of friction between the block and slab is $0.60$ while the kinetic friction is $0.40$. The $10 \,kg$ block is acted upon by a horizontal force $100 \,N$. If $g = 9.8 \,m/s^2$,the resulting acceleration of the slab will be ........ $m/s^2$.

Two blocks ($m = 0.5\, kg$ and $M = 4.5\, kg$) are arranged on a horizontal frictionless table as shown in the figure. The coefficient of static friction between the two blocks is $\frac{3}{7}$. Find the maximum horizontal force $F$ that can be applied on the larger block so that the blocks move together. (Round off to the nearest integer) [Take $g = 9.8\, m/s^2$]

When $F = 2 \text{ N}$, what is the frictional force between the $5 \text{ kg}$ block and the ground (in $\text{ N}$)?

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If the acceleration of block $A$ is $2 \, m/s^2$,which is provided by the frictional force from block $B$,then the magnitude of the frictional force applied by block $B$ on block $A$ is ......... $N$.

The rear side of a truck is open and a box of $40 \;kg$ mass is placed $5 \;m$ away from the open end as shown in Figure. The coefficient of friction between the box and the surface below it is $0.15$. On a straight road,the truck starts from rest and accelerates with $2 \;m s^{-2}$. At what distance from the starting point does the box fall off the truck? (Ignore the size of the box).

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