I think the strangest thing in the universe is the mind of human being and more precisely the consciousness. Any amount of research in this is further complicating the matter. It can be said to be beyond the scope of science. It is the strangest.

Also, 'I' section has got a higher moment of inertia than many other symmetrical section of same cross sectional area. In a beam the stresses are max. at extreme points(ie. above and below the centre)

I think since the bodies are perfectly rigid during the colision there will not be any transfer of energy which requires deformation of the body. As a result the magnitude of the momentum and KE of the individual masses will remain same. Ofcourse there will be a reversal of direction.

Solid Angle also has got a unit namely sterradian but no dimension.

Q1) There is a friction between the table cloth and dish. When you pull slowly the the dish the inertial force (mass into acceleratin) will be less than this friction force. So dish will follow the table cloth. When you pull fast the friction force will not be sufficient to carry the dish along with this due to inertia(mass x acceleration) as acceleration here is higher.

Q2) Yes , action and reaction get cancelled when they are acting on the same body. Eg: When you push a car sitting inside it your action and reaction get cancelled and car doesn't move.

Q3) Earth moon system is revolving around sun where centrifugal force and sun's attraction are balanced. It is in a state of free fall. So ot won't fall in  to sun. Similarly moon is revolving around earth like a satellite. So as such there is no net force on sun-earth-moon system and it is in a balanced condition.

Q4)  See v^2 =2 a S

If v increases by 50% S increases by 125%

Q5) When you are descend at constant speed your acceleration is prevented by some brakes in the elevator and it gets heated up.

Q6) I have no idea

Q7) With a single mass it is not possible but in a system like recoiling gun it is possible. Gun and bullet will have KE.But total momentum is zero. 

I think the questioner wants to know why bones are not deforming or elongating during accidents but mostly fractured.

It may be because basically bone is a brittle material which cannot be deformed. Where as ductile material can be deformed.

I think it is also a blessing in disguise. If our bones were flexible and ductile our shapes will change after accidents and it may do irreparable damages!

I think then the change in frequency will be varying and formula in terms of velocity will still hold good. So it will be a continously varying pitch.

When a speeding train passes the whistle sound frequency changes abruptly due to change in the direction of velocity which is nothing but a sort of instant acceleration.

Answer given by coolvignesh  is right I think.

It willl be easy to understand if we consider two halves of ring where net centrifugal force on both halves will cause a tension in the ring in tangential direction at two places where they  meet.

A circular ring  rotating at uniform angular velocity doesn't require any further force for continuing the rotation provided there is no friction.

I think it will be cylindrical.Assuming that there is atmosphere, the gas will continue to come out of the nozzle due to pressure and will move in same direction after burning in same shape(cross section) . The speed of outflowing gas will remain same due to its initial momentum as there is no buoyancy force. But flame will be seen only to certain height since temperature goes down. So overall it will appear like a cylinder.

Can't we explain it this way?

The flame is nothing but gas at a high temperature and hence low in density compared to the surrounding air. Now due to buoyancy force this hot gas moves up like hydrogen balloon. The flame is seen to a limited height because the temperature comes down to the threshold value. Flame is narrowing down because of an increase in velocity initially when gas moves up(Area of cross section comes down when flow velocity  increases) . It could also be due to cooling.

Let  u=speed of car in m/min

       v= speed of man in m/min

       t1=usual time car takes to reach factory from station in min.

        t2= time spent by engineer in walking in min (to be determined)

         t3= time taken by car to reach factory after picking the engineer on the way in min

Now

       t2+t3 = 60 + t1 - 10

       t1-t3 = t2 - 50

Cosidering distances covered

     v . t2 = u (t1 - t3)      ( Because car travelled so much distance less that day)

       v t2 =u (t2 - 50)    ( From above)

        v/u  = 1 -50/t2

We know that  car reached that day 10 mts early. So car saved traveling twice the distance travelled by man by avoiding to and fro driving.

Hence    10 u =2 t2 v  (car would have travelled additional 10 min had the engineer not walked)

                      v/u =5/t2

Substituting v/u from above  we get

         1 - 50/t2 = 5/t2

    t2 -50 =  5

    t2  = 5 + 50 = 55 min

 I hope it is right!  May be there is a shorter way of doing it !

I think no  snakes will die. All the snakes are moving . So these snakes can only bite same portion always. They can't advance since the relative speed  is zero. So the circle cannot become smaller and smaller. But questioner has not clearly told whether the speeds of snakes are same. 

See log₇ 343 =3 ,So this is the first intiger with characteristics of log equals to 3.  (1 X 7³ =343)

log₇ 2401 =4   So naturally the characteristics of 2401-1  will be 3. Because 2401 is the first intiger with characteristic value equal to 4.

So total number of intigers between 343 and 2401 is 2058.

I hope it is clear now.  If u think about a problem with base 10 , it easier to follow.

Which is the best book that gives complete questions and solutions of last 30 yrs of JEE year wise?

A mirror of height 4h/3 has to be kept at a height of 4h/3 above floor. Is it right?