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

A mass of $1 \mathrm{kg}$ is suspended by a thread. It is–
(i) lifted up with an acceleration $4.9\mathrm{m}{\mathrm{s}}^{-2},$
(ii) lowered with an acceleration $4.9\mathrm{m}{\mathrm{s}}^{-2}.$
The ratio of the tensions in (i) and (ii) is 

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 :