Newton's Laws of Motion

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 $\left(g=9.8 \mathrm{m} {\mathrm{s}}^{-2}\right)$

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 $C$?

State Newton's first law of motion.

Three forces acting on a body are shown in the figure. To have a resultant force only along the $Y-\mathrm{axis}$, the magnitude of the minimum additional force needed is:

The rough surface of a horizontal table offers a definite maximum opposing force to initiate the motion of a block along the table, which is proportional to the resultant normal force given by the table. Forces $\mathrm{F}1$ and $\mathrm{F}2$ act at the same angle $\mathrm{\theta }$ with the horizontal and both are just initiating the sliding motion of the block along the table. Force $\mathrm{F}1$ is a pulling force while the force $\mathrm{F}2$ is a pushing force. $\mathrm{F}2 > \mathrm{F} 1$ , because

Consider following forces: $\left(\mathrm{w}\right)$ Force due to tension along a string,$\left(\mathrm{x}\right)$ Normal force given by a surface, $\left(\mathrm{y}\right)$ Force due to air resistance and $\left(\mathrm{z}\right)$Buoyant force or upthrust given by a fluid. Which of these are electromagnetic forces?

A bullet of mass $40 \mathrm{g}$moving with a speed of $90\mathrm{ }\mathrm{m}\mathrm{ }{\mathrm{s}}^{-1}$ enters heavy wooden block and is stopped after a distance of $60 \mathrm{cm}$. What is the average resistive force exerted by the block on the bullet $x \mathrm{N}$. The value of $x$ is

A small spherical ball (obeying Stoke's law for viscous force) is thrown up vertically with a speed $20 \mathrm{m} {\mathrm{s}}^{-1}$ and is received back by the thrower at the point of projection with a speed $10 \mathrm{m} {\mathrm{s}}^{-1}$. Neglecting the buoyant force on the ball, assuming the speed of the ball during its flight to be never equal to its terminal speed and taking the acceleration due to gravity $\mathrm{g}=10 \mathrm{m} {\mathrm{s}}^{-2}$, find the time of flight of the ball in seconds.

The momentum of a system of particles is always conserved. True or false?

Can a single isolated force exist in nature? Explain your answer.