Embibe Experts Solutions for Chapter: Friction, Exercise 2: Exercise - 2

A uniform rope lies on a table with some portion hanging. The rope begins to slide when the length of the hanging part is $25\%$ of the entire length. The coefficient of friction between rope and table is:

Given $m_{\mathit{A}}=30 \mathrm{kg}, m_{\mathit{B}} = 10 \mathrm{kg}, m_{\mathit{C}}=20 \mathrm{kg}$. Between $A$ and $B$ friction coefficient ${\mathrm{\mu }}_1 = 0.3$, between $B$ and $C$ friction coefficient ${\mathrm{\mu }}_2 = 0.2$ and between $C$ and ground ${\mathrm{\mu }}_3 = 0.1$. The least horizontal force $F$ to start the motion of any part of the system of three blocks resting upon one another as shown in the figure is $(g=10 \mathrm{m} {\mathrm{s}}^{-2})$

The rear side of a truck is open and a box of $40 \mathrm{kg}$ mass is placed $5 \mathrm{m}$ away from the open end as shown in the 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 $2 \mathrm{m} {\mathrm{s}}^{–2}$. Find the distance (in $\mathrm{m}$) travelled by the truck by the time box falls from the truck. (Ignore the size of the box).

What is the maximum value of the force $F$ (in Newton) such that the block shown in the arrangement, does not move?

In the figure shown, the coefficient of static friction between $C$ and ground is $0.5$, coefficient of static friction between $A$ and $B$ is $0.25$, coefficient of static friction between $B$ and $C$ is zero. Find the minimum value of force $F$ (in Newton), to cause sliding between $A$ and $B$. Masses of $A, B$ and $C$ are respectively $2 \mathrm{kg}, 4 \mathrm{kg}$ and $5 \mathrm{kg}$. (Take $g=10 \mathrm{m} {\mathrm{s}}^{-2}$)

A small body was launched up an inclined plane set at an angle $\mathrm{\alpha }=15°$ against the horizontal. The coefficient of friction is $k$, if the time of the ascent of the body is $\mathrm{\eta }=2.0$ times less than the time of its descent. Find value of $100k$.

A block of mass $15 \mathrm{kg}$ is resting on a rough inclined plane as shown in the figure. The block is tied up by a horizontal string which has a tension of $50 \mathrm{N}$. The coefficient of friction between the surfaces of contact may be $(g= 10 \mathrm{m} {\mathrm{s}}^{-2})$

Car is accelerating with acceleration $=20 \mathrm{m} {\mathrm{s}}^{-2}$. A box of mass $m=10 \mathrm{kg}$ that is placed inside the car, it is put in contact with the vertical wall of car as shown. The friction coefficient between the box and the wall is $\mathrm{\mu }=0.6$. Take $g=10 \mathrm{m} {\mathrm{s}}^{-2}$.