Hi,

I have a few that u guys may already know. Here goes :-

 

1)  loss of energy in an inelastic collision

= [m₁m₂ (v₁-v₂)²(1-e)² ] / 2(m₁+m₂)

 

2)  fraction of KE transferred in an elastic collision where ,m₁=m; m₂=xm

=4x / (1+x)²

 

3)  if a bullet or any body loses f fraction of velocity after every collision with a plank, then no. of planks required to stop the bullet=1 / (1-(1-f)²)

 

4)  a body is projected from a step (stair has 'n' steps) of height 'h'and breadth 'b'. if the body hits the nth step, then square of projection velocity u²=ngb² / 2h

 

5)  dx / x(1+xⁿ) = (1/n) log(xⁿ/1+xⁿ) +c

 

6)  IF cos^-1x + cos^-1y + cos^-1z=pi, then x²+y²+z²+2xyz = 1

7)  IF sin^-1x + sin^-1y + sin^-1z=pi, then x(1-x²)+y(1-y²)+z(1-z²) = 2xyz

8)  IF tan^-1x + tan^-1y + tan^-1z=pi, then x+y+z=xyz

9)  tan^-1(x/y) + tan^-1(y-x / y+x) = pi/4

10)  IF tan^-1x + tan^-1y =pi/2 or cot^-1x + cot^-1y = pi/2, then xy=1

 

Cheers.