Constraint Relations

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? $\left(g=10 \mathrm{m}{s}^{-2}\right)$

In the arrangement shown in the figure, the points $P$ and $Q$ of the two inextensible strings move downwards with uniform speed $u$. If the pulleys $A$ and $B$ are fixed, then the mass $M$ moves upwards with a speed

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 infinitely long rods are arranged on a plane making an angle $\theta$ with each other, as shown in the figure. The rod B starts to move with a uniform velocity $\overrightarrow{v},$ in a direction perpendicular to rod $A\mathit{.}$ Thus, the point of intersection $P$ moves with a horizontal velocity ${\overrightarrow{v}}_P.$ Which of the following statements is true ?

A block of mass $M$ is pulled along a horizontal frictionless surface by a rope of mass $m$. If a force $p$ is applied at the free end of the rope, the force exerted by the rope on the block is

Three masses are connected as shown in the figure, are placed on a horizontal frictionless surface and pulled by a force of $60 \mathrm{N}$. The tensions $T_1$ and $T_2$ are in the ratio:

A monkey of mass 40 Kg  climbs on a massless rope which can stand a maximum tension of $500 \mathrm{N}$. In which of the following cases will the rope breaks? (Take $\mathrm{g}=10 {\mathrm{ms}}^{-2}$)

The force on the ceiling is,

A block of mass $M$ placed on a frictionless horizontal table is pulled by an other block of mass $m$ hanging vertically by a massless string passing over a frictionless pulley. The tension in the string is

In the following arrangement, the system is initially at rest. The $5 \mathrm{kg}$block is now released. Assuming the pulleys and string to be massless and smooth. If the acceleration of block $\mathrm{C}$ is $\frac{x}{10} \mathrm{m} {\mathrm{s}}^{-2}$, then find the value of $x$. Take $\mathrm{g}=9.8\mathrm{ }\mathrm{m} {\mathrm{s}}^{-2}$.

As shown in the figure, two particles, each of mass $\text{'}m\text{'}$ tied at the ends of a light string of length $2a$ are kept on a frictionless horizontal surface. When the mid point $\left(P\right)$ of the string is pulled vertically upwards with a small but constant force $F,$ the particles move towards each other on the surface. Magnitude of acceleration of each particle, when the separation between them becomes $2x$ is $\frac{F}{2m}\frac{x}{\sqrt{a^2-x^2}}$

Two blocks of masses $1 \mathrm{kg}$ and $2 \mathrm{kg}$ are placed on a horizontal surface and then connected to a light movable pulley as shown in the figure. A time varying force $F=4t \mathrm{N}$ starts acting on the pulley in the direction shown. Find the time (in $\sec$) after which any block will break off from the surface.

A block of mass $m$ resting on a $\theta$ wedge of angle as shown in the figure. The wedge is given an acceleration a towards left. What is the minimum value of a due to external agent so that the mass $m$ falls freely ?

A light string passing over a smooth light pulley connects two blocks of masses m1 and m2 (vertically). If the acceleration of the system is $g/8,$ then the ratio of the masses is :

Two masses of $10 \mathrm{kg}$ and $20 \mathrm{kg}$ respectively are connected by a massless spring as shown in the below figure. A force of $200 \mathrm{N}$ acts on the $20 \mathrm{kg}$ mass. At the instant shown the $10 \mathrm{kg}$ mass has acceleration $12 \mathrm{m}/{\mathrm{s}}^2$. What is the acceleration of $20 \mathrm{kg}$ mass ?