Current Affairs JEE Main & Advanced

(1) When a large force works on a body for very small time interval, it is called impulsive force. An impulsive force does not remain constant, but changes first from zero to maximum and then from maximum to zero. In such case we measure the total effect of force. (2) Impulse of a force is a measure of total effect of force. (3) \[\overrightarrow{I\,}=\int_{{{t}_{1}}}^{{{t}_{2}}}{\overrightarrow{F}\,dt}\]. (4) Impulse is a vector quantity and its direction is same as that of force. (5) Dimension : [\[ML{{T}^{-1}}\]] (6) Units : Newton-second or Kg-m-\[{{s}^{-1}}\] (S.I.)                  Dyne-second or gm-cm-\[{{s}^{-1}}\] (C.G.S.) (7) Force-time graph : Impulse is equal to the area under F-t curve. If we plot a graph between force and time, the area under the curve and time axis gives the value of impulse.      \[I\ =\]Area between curve and time axis         \[=\ \frac{1}{2}\ \times \] Base \[\times \] Height         \[=\ \frac{1}{2}\ F\ t\]   (8) If \[{{F}_{av}}\] is the average magnitude of the force then      \[I=\int_{\,{{t}_{1}}}^{\,{{t}_{2}}}{F\,dt}={{F}_{av}}\int_{\,{{t}_{1}}}^{\,{{t}_{2}}}{dt}={{F}_{av}}\Delta t\] (9) From Newton's second law \[\overset{\to }{\mathop{F}}\,=\frac{d\overrightarrow{p}}{dt}\] or            \[\int_{\,{{t}_{1}}}^{\,{{t}_{2}}}{\overrightarrow{F}\,dt}=\int_{\,{{p}_{1}}}^{\,{{p}_{2}}}{d\overrightarrow{p}}\] \[\Rightarrow \]\[\vec{I}={{\overrightarrow{p}}_{2}}-{{\overrightarrow{p}}_{1}}=\overrightarrow{\Delta p}\]   i.e. The impulse of a force is equal to the change in momentum. This statement is known as Impulse momentum theorem. Examples : Hitting, kicking, catching, jumping, diving, collision etc. In all these cases an impulse acts. \[I=\int{{}}F\,dt={{F}_{av}}.\,\Delta t=\Delta p=\]constant So if time of contact \[\Delta t\] is increased, average force is decreased (or diluted) and vice-versa. (i) In hitting or kicking a ball we decrease the time of contact so that large force acts on the ball producing greater acceleration. (ii) In catching a ball a player by drawing his hands backwards increases the time of contact and so, lesser force acts on his hands and his hands are saved from getting hurt. (iii) In jumping on sand (or water) the time of contact is increased due to yielding of sand or water so force is decreased and we are not injured. However if we jump on cemented floor the motion stops in a very short interval of time resulting in a large force due to which we are seriously injured. (iv) An athlete is advised to come to stop slowly after finishing a fast race, so that time of stop increases and hence force experienced by him decreases. (v) China wares are wrapped in straw or paper before packing.  

(1) A frame in which an observer is situated and makes his observations is known as his 'Frame of reference'. (2) The reference frame is associated with a co-ordinate system and a clock to measure the position and time of events happening in space. We can describe all the physical quantities like position, velocity, acceleration etc. of an object in this coordinate system. (3) Frame of reference are of two types :  (i) Inertial frame of reference  (ii) Non-inertial frame of reference. (i) Inertial frame of reference : (a) A frame of reference which is at rest or which is moving with a uniform velocity along a straight line is called an inertial frame of reference. (b) In inertial frame of reference Newton's laws of motion holds good. (c) Inertial frame of reference are also called unaccelerated frame of reference or Newtonian or Galilean frame of reference. (d) Ideally no inertial frame exist in universe. For practical purpose a frame of reference may be considered as inertial if it's acceleration is negligible with respect to the acceleration of the object to be observed. (e) To measure the acceleration of a falling apple, earth can be considered as an inertial frame. (f) To observe the motion of planets, earth can not be considered as an inertial frame but for this purpose the sun may be assumed to be an inertial frame. Example : The lift at rest, lift moving (up or down) with constant velocity, car moving with constant velocity on a straight road. (ii) Non-inertial frame of reference (a) Accelerated frame of references are called non-inertial frame of reference. (b) Newton's laws of motion are not applicable in non-inertial frame of reference. Example : Car moving in uniform circular motion, lift which is moving upward or downward with some acceleration, plane which is taking off.  

To every action, there is always an equal (in magnitude) and opposite (in direction) reaction. (1) When a body exerts a force on any other body, the second body also exerts an equal and opposite force on the first. (2) Forces in nature always occurs in pairs. A single isolated force is not possible. (3) Any agent, applying a force also experiences a force of equal magnitude but in opposite direction. The force applied by the agent is called 'Action' and the counter force experienced by it is called 'Reaction'. (4) Action and reaction never act on the same body. If it were so, the total force on a body would have always been zero i.e. the body will always remain in equilibrium. (5) If \[{{\overrightarrow{F}}_{AB}}\]= force exerted on body A by body B (Action) and \[{{\overrightarrow{F}}_{BA}}\]= force exerted on body B by body A (Reaction) Then according to Newton?s third law of motion \[{{\overrightarrow{F}}_{AB}}=-{{\overrightarrow{F}}_{BA}}\]  (6) Example : (i) A book lying on a table exerts a force on the table which is equal to the weight of the book. This is the force of action. The table supports the book, by exerting an equal force on the book. This is the force of reaction. As the system is at rest, net force on it is zero. Therefore force of action and reaction must be equal and opposite. (ii) Swimming is possible due to third law of motion. (iii) When a gun is fired, the bullet moves forward (action). The gun recoils backward (reaction) (iv) Rebounding of rubber ball takes place due to third law of motion.                   (v) While walking a person presses the ground in the backward direction (action) by his feet. The ground pushes the person in forward direction with an equal force (reaction). The component of reaction in horizontal direction makes the person move forward.            (vi) It is difficult to walk on sand or ice.            (vii) Driving a nail into a wooden block without holding the block is difficult.  

(1) If all the forces working on a body are acting on the same point, then they are said to be concurrent. (2) A body, under the action of concurrent forces, is said to be in equilibrium, when there is no change in the state of rest or of uniform motion along  a straight line. (3) The necessary condition for the equilibrium of a body under the action of concurrent forces is that the vector sum of all the forces acting on the body must be zero. (4) Mathematically for equilibrium \[\sum{{{{\overset{\scriptscriptstyle\rightharpoonup}{F}}}_{\text{net}}}=0}\]  or   \[\sum{{{F}_{x}}=0}\]; \[\sum{{{F}_{y}}=0}\]; , \[\sum{{{F}_{z}}=0}\] (5) Three concurrent forces will be in equilibrium, if they can be represented completely by three sides of a triangle taken in order.               (6) Lami's Theorem : For three concurrent forces in equilibrium \[\frac{{{F}_{1}}}{\sin \alpha }=\frac{{{F}_{2}}}{\sin \beta }=\frac{{{F}_{3}}}{\sin \gamma }\]    

(1) Force is an external effect in the form of a push or pull which (i) Produces or tries to produce motion in a body at rest. (ii) Stops or tries to stop a moving body. (iii) Changes or tries to change the direction of motion of the body.   Various condition of  force application

	Body remains at rest. Here force is trying to change the state of rest.
	Body starts moving. Here force changes the state of rest.
	In a small interval of time, force increases the magnitude of speed and direction of motion remains same.
	In a small interval of time, force decreases the magnitude of speed and direction of motion remains same.
	In uniform circular motion only direction of velocity changes, speed remains constant. Force is always perpendicular to velocity.
	In non-uniform circular motion, elliptical, parabolic or hyperbolic motion force acts at an angle to the direction of motion. In all these motions. Both magnitude and direction of velocity changes.

(2) Dimension : Force = mass x acceleration      \[[F]=[M][L{{T}^{-2}}]=[ML{{T}^{-2}}]\] (3) Units :  Absolute units : (i) Newton (S.I.) more...

(1) The rate of change of linear momentum of a body is directly proportional to the external force applied on the body and this change takes place always in the direction of the applied force. (2) If a body of mass m, moves with velocity \[\vec{v}\] then its linear momentum can be given by\[\vec{p}=m\vec{v}\] and if force \[\overset{\to }{\mathop{F}}\,\] is applied on a body, then            \[\vec{F}\propto \frac{d\vec{p}}{dt}\Rightarrow F=K\frac{d\vec{p}}{dt}\] or \[\vec{F}=\frac{d\vec{p}}{dt}\]                         (K = 1 in C.G.S. and S.I. units) or                 \[\vec{F}=\frac{d}{dt}(m\vec{v})=m\frac{d\vec{v}}{dt}=m\vec{a}\]        (As \[a=\frac{d\vec{v}}{dt}=\]acceleration produced in the body) \[\therefore \] \[\vec{F}=m\vec{a}\]    Force = mass ´ acceleration  

A body continue to be in its state of rest or of uniform motion along a straight line, unless it is acted upon by some external force to change the state. (1) If no net force acts on a body, then the velocity of the body cannot change i.e. the body cannot accelerate. (2) Newton's first law defines inertia and is rightly called the law of inertia. Inertia are of three types : Inertia of rest, Inertia of motion and Inertia of direction.            (3) Inertia of rest : It is the inability of a body to change by itself, its state of rest. This means a body at rest remains at rest and cannot start moving by its own. Example : (i) A person who is standing freely in bus, thrown backward, when bus starts suddenly. When a bus suddenly starts, the force responsible for bringing bus in motion is also transmitted to lower part of body, so this part of the body comes in motion along with the bus. While the upper half of body (say above the waist) receives no force to overcome inertia of rest and so it stays in its original position. Thus there is a relative displacement between the two parts of the body and it appears as if the upper part of the body has been thrown backward. Note : 

• (i) If the motion of the bus is slow, the inertia of motion will be transmitted to the body of the person uniformly and so the entire body of the person will come in motion with the bus and the person will not experience any jerk.           

(ii) When a horse starts suddenly, the rider tends to fall backward on account of inertia of rest of upper part of the body as explained above. (iii) A bullet fired on a window pane makes a clean hole through it, while a ball breaks the whole window. The bullet has a speed much greater than the ball. So its time of contact with glass is small. So in case of bullet the motion is transmitted only to a small portion of the glass in that small time. Hence a clear hole is created in the glass window, while in case of ball, the time and the area of contact is large. During this time the motion is transmitted to the entire window, thus creating the cracks in the entire window. (iv) In the arrangement shown in the figure : (a) If the string B is pulled with a sudden jerk then it will experience tension while due to inertia of rest of mass M this force will not be transmitted to the string A and so the string B will break. (b) If the string B is pulled steadily the force applied to it will be transmitted from string B to A through the mass M and as tension in A will be greater than more...

(1) Linear momentum of a body is the quantity of motion contained in the body. (2) It is measured in terms of the force required to stop the body in unit time. (3) It is also measured as the product of the mass of the body and its velocity i.e., Momentum = mass × velocity. If a body of mass m  is moving with velocity \[\overrightarrow{v\,}\] then its linear momentum \[\overrightarrow{p}\]is given by \[\overrightarrow{p}=m\,\overrightarrow{v\,}\] (4) It is a vector quantity and it?s direction is the same as the direction of velocity of the body. (5) Units : kg-m/sec [S.I.],  g-cm/sec [C.G.S.] (6) Dimension : \[[ML{{T}^{-1}}]\] (7) If two objects of different masses have same momentum, the lighter body possesses greater velocity.           \[\therefore \] \[p={{m}_{1}}{{v}_{1}}\]\[={{m}_{2}}{{v}_{2}}\]= constant    \[\frac{{{v}_{1}}}{{{v}_{2}}}=\frac{{{m}_{2}}}{{{m}_{1}}}\]    i.e.  \[v\propto \frac{1}{m}\]                  [As p is constant] (8) For a given body \[p\,\propto v\]        (9) For different bodies moving with same velocities \[p\,\propto \,m\]              

(1) Inherent property of all the bodies by virtue of which they cannot change their state of rest or uniform motion along a straight line by their own is called inertia. (2) Inertia is not a physical quantity, it is only a property of the body which depends on mass of the body. (3) Inertia has no units and no dimensions (4) Two bodies of equal mass, one in motion and another is at rest, possess same inertia because it is a factor of mass only and does not depend upon the velocity.  

(1) An object can be considered as a point object if during motion in a given time, it covers distance much greater than its own size. (2) Object with zero dimension considered as a point mass. (3) Point mass is a mathematical concept to simplify the problems.