Applications of Newton's Laws of Motion

The coefficient of static friction, ${\mu }_s$, between block $A$ of mass $2 \mathrm{kg}$ and the table as shown in the figure is $0.2$. What would be the maximum mass value of block $B$ so that, the two blocks do not move? The string and the pulley are assumed to be smooth and massless $\left(\mathrm{g}=10 {\mathrm{ms}}^{-2}\right)$.

A monkey of mass $20 \mathrm{kg}$ is holding a vertical rope. The rope will not break when a mass of $25 \mathrm{kg}$ is suspended from it, but will break if the mass exceeds $25 \mathrm{kg}$. What is the maximum acceleration with which the monkey can climb up along the rope? $\left(g=10 \mathrm{m}{s}^{-2}\right)$

The pulley arrangements of the figure. (a) and (b) are identical. The mass of the rope is negligible. In (a) the mass $m$ is lifted up by attaching a mass $2m$ to the other end of the rope. In (b), $m$ is lifted up by pulling the other end of the rope with a constant downward force  $F=2mg$. The acceleration of $m$ in both cases is?

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 magnitude and direction of the force of friction acting on $A.$

Two masses  $m_1=5 \mathrm{kg}$ and  $m_2=4.8 \mathrm{kg}$ tied to a string are hanging over a light frictionless pulley. What is the acceleration of the masses when left free to move? ($g=9.8 \mathrm{m} {\mathrm{s}}^{-2}$ )

A particle starts sliding down a frictionless inclined plane. If $S_n$ is the distance travelled by it from time $t=(n-1)$ $\sec$ to $t=n$ $\sec$, the ratio $\frac{S_n}{S_{n+1}}$ is

Two blocks of mass$2 \mathrm{kg}$ and$3 \mathrm{kg}$are arranged as shown and released from rest. Assuming string and pulley to be ideal, find the separation between them after$1 \sec$ [$g=10 \mathrm{m} {\mathrm{s}}^{-2}$]

If acceleration of block $A$ in case $1$ is $a_1$ and in case $2$ is $a_2$, then $a_1:a_2$ is

In the system of pulleys shown what should be the value of $m_1$ such that $100 \mathrm{g}$ remains at rest: (Take $g=10 \mathrm{m} {\mathrm{s}}^{-2}$)

A block of mass $5 \mathrm{kg}$ starting from rest pulled up on a smooth incline plane making an angle of $30°$ with horizontal with an effective acceleration of $1 \mathrm{m} {\mathrm{s}}^{-2}$. The power delivered by the puling force at $t=10 \mathrm{s}$ from the start is _____ $\mathrm{W}$.
[Use $g=10 \mathrm{m} {\mathrm{s}}^{-2}$]
(Calculate the nearest integer value)

As per given figure, a weightless pulley P is attached on a double inclined frictionless surfaces. The tension in the string (massless) will be (if $g=10 \mathrm{m} {\mathrm{s}}^{-2}$)

Two masses $m$ and $2 m$ are connected by a mass less string which passes over a light frictionless pulley shown in the figure. The masses are initially held with equal lengths of the strings on either side of the pulley. Find the velocity of the masses at the instant the lighter mass moves up a distance of$6.54 \mathrm{m}$. This string is suddenly cut at that instant. Calculate the time taken by each mass to reach the ground. Take $g=9.8 \mathrm{m} {\mathrm{s}}^{-2}$.

A body of mass$2 \mathrm{kg}$ slides down with an acceleration of $3 \mathrm{m} {\mathrm{s}}^{-2}$ on a rough inclined plane having a slope of $30°$. The external force required to take the same body up the plane with the same acceleration will be ($g=10 \mathrm{m} {\mathrm{s}}^{-2}$)

The ratio of time period of oscillation of block in figure $1$ and figure $2$ is

Note:All the pulleys are ideal.

A box of mass $20 \mathrm{kg}$ is pushed up an inclined plane from rest with a force of $200 \mathrm{N}$. The plane makes an angle of $30°$ with the horizontal. The coefficient of kinetic friction between the plane and the box is $0.20$. Using work-energy theorem, calculate the speed of the box after it has been pushed for $10 \mathrm{m}$. Take $g=10 \mathrm{m} {\mathrm{s}}^{-2}$