Newton's Laws of Motion

The number of independent equations to solve a network is equal to _____.

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 $C$?

An object of mass $2 \mathrm{kg}$ is dropped from height $10 \mathrm{m}$ on the surface of earth. The acceleration produced in the motion of earth by the object will be

A particle of mass $m$ is moving in the $xy$-plane such that its velocity at a point $(x, y)$ is given as $\overrightarrow{v}=\alpha \left(y\stackrel{\wedge }{x}+2x\stackrel{\wedge }{y}\right)$ where $\alpha$ is a non-zero constant. What is the force $\overrightarrow{F}$ acting on the particle?

A smooth uniform rope is dragged by a force $F$ on a horizontal surface. The ratio $F$of tension$P$ and force $F$ is

The position vector of a particle related to time $t$ is given by $\overrightarrow{r}=\left(10t\hat{i}+15t^2\hat{j}+7\hat{k}\right)\mathrm{m}$. The direction of net force experienced by the particle is :

An average force of $125 \mathrm{N}$ is applied on a machine gun firing bullets each of mass $10 \mathrm{g}$ at the speed of $250 \mathrm{m} {\mathrm{s}}^{-1}$ to keep it in position. The number of bullets fired per second by the machine gun is :

A body of mass $500 \mathrm{g}$ moves along $x$-axis such that it's velocity varies with displacement $x$ according to the relation $v=10\sqrt{x} \mathrm{m} {\mathrm{s}}^{-1}$ the force acting on the body is:

A $2 \mathrm{kg}$ body starts from rest and accelerates uniformly against an opposing force of $4 \mathrm{N}$ at $4 \mathrm{m} {\mathrm{s}}^{-2}$. Work done on body in $2 \mathrm{s}$ by accelerating force is