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

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

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 $C$?

A player caught a cricket ball of mass $150 \mathrm{g}$ moving at a rate of $20 \mathrm{m} {\mathrm{s}}^{-1}$. If, the catching process is completed in $0.1 \mathrm{s}$, the force of the blow exerted by the ball on the hand of the player is equal to

One end of the carpet is bent back, then pulled backwards with constant unit velocity, just above the part of the carpet which is at rest on the floor. What is the minimum force needed to pull if the carpet has unit length and unit mass?

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?

Sand falls vertically on a conveyor belt at a rate of $0.1 \mathrm{kg} {\mathrm{s}}^{-1}$. In order to keep the belt moving at a uniform speed of $2 \mathrm{m} {\mathrm{s}}^{-1}$, the force required to be applied on the belt is:

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 body of mass $5 \mathrm{kg}$ is in equilibrium due to forces $F_1, F_2$ and $F_3$. $F_2$ and $F_3$ are perpendicular to each other. If $F_1$ is removed then find the acceleration of body. Given $F_2= 6 \mathrm{N}$ and $F_3=8 \mathrm{N}$.

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

A body of mass $m$ is revolving in a circle of radius $r$, with constant a speed $v$. Then the magnitude of change in momentum of the body after it undergone an angular displacement of $60°$ with respect to initial momentum is