Motion on Inclined Plane

Block $A$ of mass $m$ and block $B$ of mass $2m$ are placed on a fixed triangular wedge by means of a massless inextensible string and a frictionless pulley as shown in figure. The wedge is inclined at $45°$ to the horizontal on both sides. The coefficient of friction between block $A$ and the wedge is $\frac{2}{3}$ and that between block $B$ and the wedge is $\frac{1}{3}$. If the system of $A$ and $B$ is released from rest, find the acceleration of $A \& B$.

The upper half of an inclined plane with inclination $\mathrm{\varphi }$ is perfectly smooth while the lower half is rough. A body starting from rest at the top will again come to rest at the bottom if the coefficient of friction for the lower half is

Blocks $A$ and $B$ shown in the figure are connected with a bar of negligible weight. $A$ and $B$ each has mass $170 \mathrm{kg}$, the coefficient of friction between $A$ and the plane is $0.2$ and that between $B$ and the plane is$0.4$. What is the total force of friction between the blocks and the plane $\left(g=10\mathrm{ }\mathrm{m}{\mathrm{s}}^{-2}\right)$

In the figure shown, if friction coefficient of blocks $1$ and $2$ with an inclined plane is $\mathit{\text{μ}}=0.5$ and $0.4$, respectively, then find the correct statement.

A block of base $10 \mathrm{cm}\times 10 \mathrm{cm}$ and height $15 \mathrm{cm}$ is kept on an inclined plane. The coefficient of friction between them is $\sqrt{3}$. The inclination $\mathrm{\theta }$ of this inclined plane from the horizontal plane is gradually increased from $0°$. Then 

Write and explain Newton's second law of motion.

A block of mass m is lying at rest on an inclined plane having angle of inclination explain the equilibrium of the block by showing various forces acting on it.

How does the friction affect the motion of a block in an inclined plane?

A block of mass m is placed on a rough inclined plane of inclination θ kept on the floor of the lift. The coefficient of friction between the block and the inclined plane is μ. With what acceleration will the block slide down the inclined plane when the lift falls freely?

The acceleration of a body moving up a rough inclined plane when it is pulled up by a force, depends only on its mass.
Reason
Frictional force acts in the direction of the applied force.

A block is placed on a rough inclined plane of inclination force required to move parallel to the inclined plane.

A block is stationary on a rough inclined plane. How many forces are acting on the block?

A block of mass $2\mathrm{kg}$ Rests on a rough inclined plane making an angle of $30°$ With the horizontal. The coefficient of static friction between the block and the plane are $0.7.$ The frictional force on the block is

A block of mass $m$ is placed on a smooth inclined plane of inclination $\theta$ with the horizontal. The force exerted by the plane op the block has a magnitude

Two blocks $\mathrm{A}$ and $\mathrm{B}$ of equal masses are released from an inclined plane of inclination $45°$ at $t=0$. Both the blocks are initially at rest. The coefficient of kinetic friction between the block $\mathrm{A}$ and the inclined plane is $0.2$ while it is $0.3$ for block $\mathrm{B}$. Initially the block $\mathrm{A}$ is $\sqrt{2} \mathrm{m}$ behind the block $\mathrm{B}$. At what time in seconds will their front faces come in a line, (Take $g=10 \mathrm{m} {\mathrm{s}}^{-2}$)

A block of mass $m$ is placed on a rough plane with coefficient of friction ${\mu }_0=\frac{1}{\sqrt{3}}$ whose angle of inclination with the horizontal can be varied slowly as $0\le \theta \le \frac{\mathrm{\pi }}{2}$. If the block is tied with an elastic string of stiffness $K$ and $x$ be the instantaneous deformation in the string, then the correct variation of $x$ versus $\theta$ is given by

$\mathrm{A}$ particle of mass $1 \mathrm{kg}$ carrying $\mathrm{a}$ charge of $0.01 \mathrm{C}$ is able to remain at rest on $\mathrm{a}$ rough inclined plane of inclination $30°$ when a uniform horizontal electric field of $\frac{490}{\sqrt{3}} {\mathrm{Vm}}^{-1}$ is applied. Coefficient of friction is (Acceleration due to gravity $=9.8 \mathrm{m} {\mathrm{s}}^{-2}$)

A block of mass $2 \mathrm{kg}$ rests on a rough inclined plane making an angle of $30°$ with the horizontal. The coefficient of static friction between the block and the plane is $0.7.$ The frictional force on the block is

(Assume $\mathrm{g}=10 \mathrm{m} {\mathrm{s}}^{-2}$)

Find the maximum value of $(\mathrm{M}/\mathrm{m})$ in the situation shown in figure so that the system remains at rest. Friction coefficient of both the contact is $\mu ,$ string is massless and pulley is frictionless.