Limiting Friction

Q. In the figure shown, the coefficient of static friction between $B$ and the wall is $\frac{2}{3}$ and the coefficient of kinetic friction between $B$ and the wall is $\frac{1}{3}$. Other contacts are smooth. If the minimum force ${}^{\prime }{F}^{\prime }$ required to lift $B$ up is $\frac{xmg}{2}$, then find $x$. Mass of $A$ is $2m$ and the mass of $B$ is $m$. Take $\tan \theta =\frac{3}{4}$.

Q. A $3\text{kg}$ block is pulled by a force which is inclined at ${37}^{\circ }$ to the horizontal table. The friction coefficient between the table and block is 1/3. For what minimum value of this force, will the block start sliding?

1. $5\text{N}$
2. $10\text{N}$
3. $20\text{N}$
4. $25\text{N}$

Q. An ant starts crawling from the bottom of a bowl of radius $r$, having coefficient of friction $\mu$. The maximum vertical height $h$ up to which it can reach is

1. $r[1+\frac{1}{\sqrt{1+{\mu }^2}}]$
2. $r[1-\frac{1}{\sqrt{1+{\mu }^2}}]$
3. $r[1+\frac{1}{\sqrt{1-{\mu }^2}}]$
4. $r[1-\frac{1}{\sqrt{1-{\mu }^2}}]$

Q. A force $F$ is applied on a block of mass $75\text{kg}$ at an angle of ${53}^{\circ }$with the horizontal. If the coefficient of friction between the floor and the block is $0.6$, then what is the maximum value of force $F$ that can be applied before the block starts moving?

1. $450\text{N}$
2. $750\text{N}$
3. $500\text{N}$
4. $416.66\text{N}$

Q. Assertion: On a rainy day it is difficult to drive a car or bus at high speed.
Reason: The value of coefficient of friction is lowered due to wetting of the surface.

1. Assertion is correct but Reason is incorrect
2. Both Assertion and Reason are correct but Reasion is not the correct explanation for Assertion
3. Both Assertion and Reason are correct and Reasion is the correct explanation for Assertion
4. Both Assertion and Reason are incorrect

Q. Find the minimum value of coefficient of friction between the $4kg$ block and the surface for the system to be at rest for the figure shown.

1. $0.4$
2. $0.5$
3. $0.6$
4. $0.75$

Q. A block of mass $50kg$ can slide on a rough horizontal surface. The coefficient of friction between the block and the surface is $0.6$. The least force of pull acting at an angle of ${30}^{\circ }$ from the horizontal which causes the block to just slide is

1. $600$
2. $\frac{\sqrt{3}+0.6}{600}$
3. $\frac{600}{\sqrt{3}+0.6}$
4. $\frac{600}{\sqrt{3}-0.6}$

Q. A solid cube of mass $5kg$ is placed on a rough horizontal surface, in $xy-$plane as shown. The friction coefficient between the surface and the cube is $0.4$. An external force
$\overrightarrow{F}=6\hat{i}+8\hat{j}+20\hat{k}N$ is applied on the cube.(use $g=10m/s^2$ )

1. The block starts slipping over the surface
2. The friction force on the cube by the surface is $10N$
3. The friction force acts in $xy-$plane at angle ${127}^0$ with the positive $x-$ axis in clockwise direction
4. The contact force exeerted by the surface on the cube is $10\sqrt{1}0N$

Q. A marble block of mass $2kg$ lying on ice when given a velocity of $6m/s$ is stopped by friction in $10s$. Then the coefficient of friction is

1. $0.01$
2. $0.02$
3. $0.03$
4. $0.06$

Q. A block of mass $3kg$ is placed on the floor of coefficient of static friction is $0.4$. The force of $3.5N$ applied on the block. Calculate the force of friction and discuss the motion of the body.

1. $3.5N$, moves
2. $3.5N$, remains at rest
3. $11.76N$, moves
4. $11.76N$, remains at rest