(C) The maximum acceleration $a_{\max}$ that the block of mass $m$ can have without slipping is determined by the static friction force $f_{s, \max} =

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(C) The maximum acceleration $a_{\max}$ that the block of mass $m$ can have without slipping is determined by the static friction force $f_{s, \max} = \mu_s N = \mu_s mg$.Using Newton's second law for block $m$: $f_{s, \max} = m a_{\max} \implies \mu_s mg = m a_{\max} \implies a_{\max} = \mu_s g$.Given $\mu_s = 0.5$ and $g = 9.8 \; m/s^2$,we have $a_{\max} = 0.5 \times 9.8 = 4.9 \; m/s^2$.For the two blocks to move together,the entire system must move with an acceleration $a \le a_{\max}$.Applying Newton's second law to the combined system of mass $(m + M)$:$F = (m + M) a_{\max} = (2 + 8) \times 4.9 = 10 \times 4.9 = 49 \; N$.

Class 11 Physics Newton's Laws of Motion and Friction Block on Block System, psudo force and Constrained Motion In Friction

Medium

$A$ system of two blocks of masses $m = 2 \; kg$ and $M = 8 \; kg$ is placed on a smooth table as shown in the figure. The coefficient of static friction between the two blocks is $0.5$. The maximum horizontal force $F$ that can be applied to the block of mass $M$ so that the blocks move together will be $\dots \; N$.

JEE MAIN 2022 All JEE MAIN

A
$9.8$
B
$39.2$
C
$49$
D
$78.4$

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Class 11

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Newton's Laws of Motion and Friction

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Block on Block System, psudo force and Constrained Motion In Friction

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$A$ force of $0.5 \ N$ is applied on the upper block as shown in the figure. The coefficient of static friction between the two blocks is $0.1$ and that between the lower block and the surface is zero. The work done by the lower block on the upper block for a displacement of $3 \ m$ of the upper block is ...... $J$.

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In the arrangement shown in the figure,the coefficient of friction between the two blocks is $0.5$. The force of friction between the two blocks is (Assume that the $4 \,kg$ block is placed on a smooth horizontal surface.) (Acceleration due to gravity $= 10 \,ms^{-2}$.) (in $\,N$)

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Three blocks $A$,$B$,and $C$ of equal mass $m$ are placed on a smooth surface as shown. The coefficient of friction between any two blocks $A$,$B$,and $C$ is $\mu$. The maximum value of mass $M$ of block $D$ such that blocks $A$,$B$,and $C$ move without slipping over each other is:

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$A$ body $B$ lies on a smooth horizontal table and another body $A$ is placed on $B$. The coefficient of friction between $A$ and $B$ is $\mu$. What acceleration given to $B$ will cause slipping to occur between $A$ and $B$?

Medium

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When $F = 2 \text{ N}$,the frictional force between the $10 \text{ kg}$ block and the $5 \text{ kg}$ block is ...... $\text{ N}$. (Assume $g = 10 \text{ m/s}^2$)

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In the arrangement shown in the figure,the coefficient of friction between the two blocks is $0.5$. The force of friction between the two blocks is (Assume that the $4 \,kg$ block is placed on a smooth horizontal surface.) (Acceleration due to gravity $= 10 \,ms^{-2}$.) (in $\,N$)

Three blocks $A$,$B$,and $C$ of equal mass $m$ are placed on a smooth surface as shown. The coefficient of friction between any two blocks $A$,$B$,and $C$ is $\mu$. The maximum value of mass $M$ of block $D$ such that blocks $A$,$B$,and $C$ move without slipping over each other is:

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