(D) When the elevator accelerates downward with acceleration $a_0$,a pseudo force $ma_0$ acts upward on both blocks in the frame of the elevator.For b

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(D) When the elevator accelerates downward with acceleration $a_0$,a pseudo force $ma_0$ acts upward on both blocks in the frame of the elevator.For block $M$: The normal force $N$ is given by $N = M(g - a_0)$. The limiting friction force is $f_L = \mu N = \mu M(g - a_0)$. Since $(g - a_0) For block $m$: The effective weight is $m(g - a_0)$. The tension $T$ in the string is reduced because the effective gravitational pull is reduced. Thus,option $(B)$ is correct.For the system to accelerate,the driving force must exceed the limiting friction. The driving force is the effective weight of $m$,which is $m(g - a_0)$. The limiting friction is $\mu M(g - a_0)$. The system will accelerate if $m(g - a_0) > \mu M(g - a_0)$,which simplifies to $m > \mu M$. Thus,option $(C)$ is correct.Since all statements are correct,the correct option is $(D)$.

Class 11 Physics Newton's Laws of Motion and Friction Mix Examples-Newton's Laws of Motion and Friction

Difficult

In the figure,two blocks $M$ and $m$ are tied together with an inextensible and light string. The mass $M$ is placed on a rough horizontal surface with coefficient of friction $\mu$ and the mass $m$ is hanging vertically against a smooth vertical wall. The pulley is frictionless. Imagine a situation in which the given arrangement is placed inside an elevator that can move only in the vertical direction and compare the situation with the case when it is placed on the ground. When the elevator accelerates downward with $a_0 (< g)$,then

A
the limiting friction force between the block $M$ and the surface decreases
B
the tension in the string decreases
C
the system does not accelerate with respect to the elevator unless $m > \mu M$
D
All of the above

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Class 11

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Newton's Laws of Motion and Friction

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Mix Examples-Newton's Laws of Motion and Friction

$A$ block of mass $M = 100 \, kg$ is pulled by a force $T$ at an angle of $37^{\circ}$ with the horizontal. The coefficient of friction between the block and the ground is $\mu = 1/3$. $A$ person of mass $m = 25 \, kg$ is standing on a platform and pulls the block with the force $T$. Find the maximum upward acceleration $a_{\max}$ of the person such that the block just starts to move.

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In the figures $(i), (ii)$ and $(iii)$ shown, the objects $A, B$ and $C$ have the same mass $m$. The string, spring, and pulley are massless. Object $C$ strikes object $B$ with velocity $u$ in each case and sticks to it. Find the ratio of the velocity of $B$ in case $(i)$ to $(ii)$ to $(iii)$.

Difficult

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$A$ ball rests upon a flat piece of paper on a table top. The paper is pulled horizontally but quickly towards the right as shown. Relative to its initial position with respect to the table,the ball:
$(1)$ remains stationary if there is no friction between the paper and the ball.
$(2)$ moves to the left and starts rolling backwards,i.e.,to the left,if there is friction between the paper and the ball.
$(3)$ moves forward,i.e.,in the direction in which the paper is pulled.
Here,the correct statement$(s)$ is/are:

MediumKCET 2010

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The masses of blocks $A$ and $B$ are $100 \, kg$ and $200 \, kg$ respectively. The coefficient of friction between $A$ and $B$ is $0.2$,and the coefficient of friction between $B$ and the ground is $0.3$. What force $F$ (in $N$) must be applied to block $B$ to make it move?

Medium

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Two unequal masses $A$ and $B$ moving along a straight line are brought to rest by equal retarding forces. If $A$ takes double the time taken by $B$ to come to rest and $A$ travels $\frac{2}{3}$ of the distance covered by $B$ before coming to rest,then the ratio of masses of $A$ and $B$ is . . . . . . .

EasyAP EAMCET 2017

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In the figures $(i), (ii)$ and $(iii)$ shown, the objects $A, B$ and $C$ have the same mass $m$. The string, spring, and pulley are massless. Object $C$ strikes object $B$ with velocity $u$ in each case and sticks to it. Find the ratio of the velocity of $B$ in case $(i)$ to $(ii)$ to $(iii)$.

The masses of blocks $A$ and $B$ are $100 \, kg$ and $200 \, kg$ respectively. The coefficient of friction between $A$ and $B$ is $0.2$,and the coefficient of friction between $B$ and the ground is $0.3$. What force $F$ (in $N$) must be applied to block $B$ to make it move?

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