Total distance S = 200+300= 500m

Initial velocity u = 3m/s

Final velocity v = 5 m/s

We know, 

v^{​​​​​​2}​​​​​-u^​​​2 = 2as

=> 25-9= 1000a

=> a = {tex}{16\over 1000} m/s^2{/tex}

Again 

v = u +at

=> 5 = 3+{tex}{16\over 1000}t{/tex}

=> t = {tex}{2\times 1000\over 16 }= 125s = 2 \ minutes \ 5 \ second{/tex}

The quantity of heat Q transferred into the box  from its one face 

Q = {tex}KA(T_h–T_c)t\over d{/tex}  

where K is thermal conductivity of thermocol.

=  {tex}0.01×2500×10^{–4}×40º×5×60×60\over 4×10^{–2}{/tex} = 45000 J 

As the box has six faces, total heat passing into the box Q = 45000 × 6 J = 270000 J 

The mass m of ice melted= {tex} Q\over L {/tex} = {tex}270000\over 335{/tex} = 805.97 g

The quantity of heat transferred into the box through its one face can be obtained by equation :

Q = {tex}KA (T_h –T_c ) t\over d {/tex} = 

where K is thermal conductivity of thermocol.

A is area of one face of cube. 

{tex}T_h \ is \ outside \ temperature{/tex}

{tex}T_c \ is \ inside \ temperature{/tex}

t is time and d is thickness.

So 

=  {tex} 0.01 × 2500 × 10^{–4} × 40º  × 5 ×  60 × 60 \over 4 × 10^{–2  }{/tex} = 45000 J 

Since the box has six faces, total heat passing into the box Q = 45000 × 6 J

The mass of ice melted  m, can be obtained by dividing  Q  by  L  :

m =  Q/L ={tex}45000 × 6 \over 335{/tex} = 805.97 g

At the highest point of a projectile, the vertical component of velocity is zero and the velocity is entirely horizontal. The direction of acceleration (due to gravity) is vertically downwards throughout the motion of the projectile. Therefore, the angle between the direction of acceleration and velocity at the highest point of a projectile is 90 °
 

Mass of car m = 2000 kg = 2{tex}\times 10^3 kg{/tex}

Initial velocity u = 40km/h = {tex}{40000\over 3600 }={100\over 9}m/s{/tex}

Distance to be covered before stopping s = 4m

Final velocity v = 0 

We know

{tex}v^2-u^2= 2as{/tex}

=> {tex}{10^4\over 81}= 2a\times 4{/tex}

=> {tex}a = {1250\over 81}{/tex}m/s^{​​​​​​2}

force applied = ma = {tex} {1250\over 81} \times 2000 = 30864.19\ N{/tex}

Initial velocity u = 40km/h = {tex}{40000\over 3600 }={100\over 9}m/s{/tex}

Distance to be covered before stopping s = 4m

Final velocity v = 0 

We know

{tex}v^2-u^2= 2as{/tex}

=> {tex}{10^4\over 81}= 2a\times 4{/tex}

=> {tex}a = {1250\over 81}{/tex}m/s^{​​​​​​2}

Mass of car m = 2000 kg

force applied = ma = {tex} {1250\over 81} \times 2000 = 30864.19\ N{/tex}

m(A) = 12, m(B) = 5, m(C) = 13, where m(X) stands for magnitude of X.
A + B = C

squaring both sides,

A.A+ B.B + 2 A.B = C.C

note 'dot’ product i.e. A.A is equal to m(A)ˆ2.

=> m(A)ˆ2 + m(B)ˆ2 + 2 m(A)m(B)cos(ab) = m(C)ˆ2 , where ab is the angle between A and B.

Substituting the values in the above equation,

=> 144 + 25 + 60cos(ab) = 169

=> 169 + 60cos(ab) = 169

=> 60cos(ab) = 0

=> cos(ab) = 0

=> cos(ab) = cos(pi/2) or cos(90deg)

Here, {tex}V = 100 \pm 5V{/tex}and {tex}I = 10 \pm 0.2A{/tex}

Expressing limits of error as percentage error, we have

{tex}V = 100V \pm \frac{5}{{100}} \times 100 = 100V \pm 5\% {/tex}

{tex}I = 10A \pm \frac{{0.2}}{{100}} \times 100 = 10A \pm 2\% {/tex}

Now,{tex}R = \frac{V}{I}{/tex}

{tex}\therefore{/tex}% error in R=%error in V + % error in I

=5%+2%

=7%

{tex}\therefore{/tex}% error in R=7%

Let’s  first  find  the mean  value  of time:

{tex}t_{mean}={t_1+t_2+t_3+t_4\over 4}{/tex}

= {tex}{90+91+95+92\over 4}= 92 {/tex}

Then,  we can  find  the  absolute error for each  measurement:

{tex}\Delta t_1=|t_{mean}-t_1|= |92-90|=2{/tex}

{tex}\Delta t_2=|t_{mean}-t_2|= |92-91|=1{/tex}

{tex}\Delta t_3=|t_{mean}-t_3|= |92-92|=0{/tex}

{tex}\Delta t_4=|t_{mean}-t_4|= |92-95|=3{/tex}

Let’s  calculate the mean  absolute error: 

{tex}\Delta t_{mean}={ \Delta t_1+ \Delta t_2+ \Delta t_3+ \Delta t_4\over 4}{/tex}

= {tex}{2+1+0+3\over 4}= 1.5{/tex}{tex}\approx 2{/tex}

Therefore,  the reported  mean  time should  be  92 ± 2s

1. the tension of the surface film of a liquid caused by the attraction of the particles in the surface layer by the bulk of the liquid, which tends to minimize surface area.

In physics, a polar vector is a vector such as the radius vector r that reverses sign when the coordinate axes are reversed. Polar vectors are the type of vector usually simply known as "vectors." In contrast, pseudovectors (also called axial vectors) do not reverse sign when the coordinate axes are reversed. Examples of polar vectors include r, the velocity vector v, momentum p, and force F. The cross product of two polar vectors is a pseudovector

Two principles thrusts in the study of Physics are

• Unification which means explaining different physical phenomena by using few laws and concepts. Example: Electricity, magnetism and light are different phenomena and have different laws of physics for each of them. These are unified under theory of electromagnetism; all these three phenomena can be explained from this theory of electromagnetism.
• Reductionism which means explaining complex phenomena by breaking them into smaller constituents and studying simpler parts.

Example: A complex music can be broken down to simple sine waves so that we can make the music piece from the simple tones.

let the initial velocity of football is u m/sec motion from ground to window

v=5m/sec

h=15m

v² -u² =2gh

=> 25 -u² = 2*(-10)*15

=> u²=325

=u = {tex}\sqrt {325} = 5\sqrt{13}{/tex}m/s

A)motion from window to maximum height

 v²-u² = 2as

Here v is final velocity of ball = 0m/s

u is initial velocity of ball = 5m/s

a is acceleration due to gravity = -10 as it is going upward

s is distance traveled by it = ?

So,

=> 0 - 25 = 2*(-10)*h

=> -25 = -20h

=> h = {tex}{-25\over -20}= {5\over 4}{/tex}

Total height = 15 + {tex}{5\over 4} = {65\over 4}{/tex}m

B)motion from ground to max height

u= {tex}5\sqrt{13}{/tex}

v=0

v=u-gt

t={tex}{5\sqrt {13}\over 10}= {\sqrt {13}\over 2} sec{/tex}

{tex}v = \frac{4}{a}{/tex}(Given)

{tex}\therefore a = \frac{{dv}}{{dt}} = \frac{4}{v}{/tex}     -eqⁿ (1)

{tex}\Rightarrow\int\limits_6^v {vdv} = \int\limits_2^t {4dt} {/tex}

{tex} \Rightarrow \frac{1}{2}{v^2} - 18 = 4t - 8{/tex}

{tex} \Rightarrow {v^2} = 18t + 20{/tex}

At t=3 sec, 

v²=74

{tex}v = \pm \sqrt {74} {/tex}

Taking positive value of v

{tex}v = +6.63m/\sec {/tex}

Putting value of v in eq ⁿ (1)

{tex}a = \frac{4}{{6.63}} = 0.603m/{\sec ^2}{/tex}

A car in a steady turn has a centripetal acceleration. There is an inertial force associated with every acceleration acting in the opposite direction and in this case it is the centrifugal force. The friction at the tires arises as a centripetal force to match the centrifugal force.

Let height of tower be 'h'

Time taken for 1st stone to reach ground = {tex}\sqrt{2h\over g}{/tex}

{tex}\left[ s = ut+ {1\over 2}at^2 ;h = {1\over 2}gt^2\right]{/tex}

Time taken for the first stone to be travel 5 m from top = {tex}\sqrt{2\times 5\over g}{/tex}

Time taken for 2nd stone to reach ground from a point (h−25)m above the ground = {tex}\sqrt{2(h-25)\over g}{/tex}

So, 

{tex} \sqrt{2h\over g} -\sqrt{2\times 5\over g} = \sqrt{2(h-25)\over g}{/tex}

{tex}=> \sqrt{2h} -\sqrt{10} = \sqrt{2(h-25)}{/tex}

Squaring both sides

=> 2h + 10 - {tex}2\sqrt {20h}= {/tex}2h -50

=> {tex}\sqrt{20h} = 30{/tex}

Sqauring both sides

=> 20h = 900

=> h = 45

Ans. The connection between physics, technology and society can be seen in many examples. The discipline of thermodynamics arose from the need to understand and improve the working of heat engines. The steam engine is inseparable from the Industrial Revolution in England in the eighteenth century, which had great impact on the course of human civilisation. Sometimes technology gives rise to new physics; at other times physics generates new technology

We can understand this by some examples :

• The wireless communication technology that followed the discovery of the basic laws of electricity and magnetism in the nineteenth century.
   
• Development of Alternative Energy Resources : A most significant area to which physics has and will contribute is the development of alternative energy resources. The fossil fuels of the earth are ending fast and there is an urgent need to discover new and affordable sources of energy. Considerable progress has already been made in this direction. For example : Conversion of solar energy, geothermal energy into electricity.
   
• Silicon Chip Technology : Yet another important example of physics giving rise to technology is the silicon chip, that triggered the computer revolution in the last three decades of the twentieth century.

Ans. The fact that we do not have a final theory in science is testament to our very limited understanding of the world around as well as within us. We do not have a complete sense of apprehension about most (if not all) of the various facets of science, like the following.

• what causes life?
• are we alone In space?
• what is the final number of elements in our universe ?
  
  Many such questions plague the minds of scientists today and until all such queries are dealt with we will never have a full sense of everything. Now, even if we do happen to find the answers to everything then how do we now that there aren't any other questions left.
  
  In other words do we even completely know what lies phenomena lies uncovered for us to decipher its mechanism. It seems almost impossible to demystify all of them, let alone the unknown stuff.
  
  So, it might seem a bit pessimistic but it is almost certain that we will never have a final theory of science there are bound to be a few exceptions, but that is the fun of it all. The world would be a dull place without all its mysteries (for us to solve).

Every experiment, calculation, result and prediction starts and ends with theory. Theory and experiment go hand in hand.

Theory makes predictions and motivate experiments. Experimental results are used to update, improve and validate the framework that scientists work within.

The models are reassessed under the light of the new data. The new information then comes full circle by helping to determine which experiments are conducted next. By knowing where the gaps in knowledge are – where  theory needs more information – scientists can better decide which questions to ask and which experiments to run next.

• A hypothesis is a supposition without assuming that it is true. It would not fair to ask anybody to prove the universal law of gravitation, because it cannot be proved. It can be verified by experiments.
• An Axiom is self-evident truth
•  A Model is a theory proposed to explain observed phenomena.

Theory is a set of statements or principles devised to explain a group of facts or phenomena.

Most theories that are accepted by scientists have been repeatedly tested by experiments and can be used to make predictions about natural phenomena.