Newton’s Laws of Motion

A block of mass $m$ is placed on a smooth wedge of inclination $\theta$. The whole system is accelerated horizontally so that the block does not slip on the wedge. The force exerted by the wedge on the block ($g$ is acceleration due to gravity) will be

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 body of mass 5 kg explodes at rest into three fragments with masses in the ratio 1 : 1 : 3. The fragment with equal masses fly in mutually perpendicular directions with speeds of 21 ms^-1​. The velocity of heaviest fragment in ms^-1 will be

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

A lift weighing $1000 \mathrm{kg}$ is moving upwards with an acceleration of $1 \mathrm{m} {\mathrm{s}}^{-2}$. The tension in the supporting cable is $\left(g=9.8 \mathrm{m} {\mathrm{s}}^{-2}\right)$

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 blocks of mass $2.9 \mathrm{kg}$ and $1.9 \mathrm{kg}$ are suspended from a rigid support $S$ by two inextensible wires each of length $1 \mathrm{m}$ see figure. The upper wire has negligible mass and the lower wire has a uniform mass of $0.2 \mathrm{kg}{\mathrm{m}}^{-1}$ . The whole system of blocks, wires and support has an upward acceleration of $0.2 \mathrm{m}{\mathrm{s}}^{-2}$ . Acceleration due to gravity is $9.8 \mathrm{m}{\mathrm{s}}^{-2}$ .

(i) Find the tension $T$ at the mid-point of the lower wire.

(ii) Find the tension  $T^{\text{'}}$  at the mid-point of the upper wire.

Two cubes of masses  $m_1$ and  $m_2$ be on two frictionless slopes of block A which rests on a horizontal table. The cubes are connected by a string which passes over a pulley as shown in the figure. To what horizontal acceleration f should the whole system (that is the blocks and cubes) be subjected so that the cubes do not slide down the planes? What is the tension of the string in this situation?

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 particles of mass $m$ each are tied at the ends of a light string of length $2a.$ The whole system is kept on a frictionless horizontal surface with the string held tight so that each mass is at a distance $a$ from the centre $P$ (as shown in the figure). Now, the mid-point of the string is pulled vertically upwards with a small but constant force $F.$ As a result, the particles move towards each other on the surface. The magnitude of acceleration, when the separation between them becomes $2x,$ is

The string between blocks of mass $m$ and $2m$ is massless and inextensible. The system is suspended by a massless spring as shown. If the string is cut find the magnitudes of accelerations of mass $2m$ and $m$ (immediately after cutting)

A block $P$ of mass $m$ is placed on a horizontal frictionless plane. A second block of mass $m$ is placed on it and is connected to a spring of spring constant $k,$ the two blocks are pulled by distance $A$. Block $Q$ oscillates without slipping. What is the maximum value of frictional force between the two blocks?

Three identical blocks of masses $m=2 \mathrm{kg}$ are drawn by a force $F=10.2 \mathrm{N}$ on a frictionless surface, then what is the tension (in $\mathrm{N}$) in the string between the blocks $B$ and $C$?