Physics, Chemistry, Mathematics Forums

A vertically oriented uniform rod of mass M and lenght l can rotate about its upper end. A horizontally flying bullet of mass m strikes the lower end of the rod and gets stuck in it; as a result, the rod swings through an angle alpha. Assume that m<<M, find: (a) the velocity of the flying bullet; (b) the momentum increment in the system "bullet-rod" during the impact, what causes the change of that momentum; (c) at what distance x from the upper end of the rod the bullet must strike for the momentum of the system "bullet-rod" to remain constant during the impact.

 Ans:  a) v=M/m  root ( 2/3 gl) sin alpha/2

         b) change in momentum = M [  ((1/6 gl)^0.5)  sin alpha/2 ]

        c) x=2l/3

Please reply with explanation!

What will be the sum of the following series upto infinity.
1 +1/5*5! + 1/9*9! + 1/13*13!.....

A pulley carries weightless thread with masses m and M at its ends. The friction between pulley and thread is such that the thread starts slipping only when M/m>_/n. Find (a) the coefficient of friction and (b) the acceleration of the masses, when M/m>n

Q1.If radius of circumcircle of triangle is 10 and that of incircle is 5, then the square of the sum of radii of the escribed circles is?

Answer:2025

Q2.Please see attachment

Let a be a complex number such that |a|<1 and z₁,z₂,......,z_n be the vertices of a polygon such that z_k=1+a+a²+......a^k,then find equation of circle within which the vertices of the polygon lie. 

1.Two numbers a and b are chosen from the set{1,2.......25}. Find the probability that a^4-b^4 is divisible by 5?

2. Two numbers x and y are chosen at random(without replacenent) from among the numbers 1,2,3,....99.Find the probability that x^3-y^3 is divisible by 3?

The answer to 1 is 2/3 and to 2 is 16/49.

Hi. I am trying to solve a couple of chemistry problems relating to using the empirical formula and am struggling with it. Can someone show me how they would do it.

Here they are:

A hydrocarbon mixture consists of 88.89% carbon and 11.11% hydrogen by mass. What is the empirical formula of the hydrocarbon?

If the molecular weight of the hydrocarbon is approximately 54 g/mol, what is the molecular formula?



Thanks!

 Find the area bounded by the following curves:

1) y= arc sin(|sinx|) and y = (arc sin(|sinx|))^2 ; (0<x<2pi)

the answer i have is      4/3 + pi^2[pi/3-1/2]

1) Solve the following:

\(\int {\sin x^1/2/xdx}\) (limit from 0 to 1)

2) How many real roots does the following equation have:

x^7 + x^6 + x^5 + x^4 + x^3 + x^3 + x^2 + x^1 + 1=0

I dont have an answer for this question, did it as following .Is it right

Since this is a geometric progression the above expression can be written as
(x^7-1)/(x-1)=0 , now for no value of x this equation is satisfied because at x=1 it will be undefined .therefore no real roots for this equation.

A turn table of mass M and radius R is rotating with angular velocity omega knot on frictionless bearing. A spider of mass m falls vertically onto the rim of the turn table and then walks in slowly towards the centre of the table. What is the angular velocity of the system when spider is at a distance r from the centre. Compute also the angular velcoity of the turn table when the spider is at the rim . Is the energy of the system in this problem conserved?

Ans : omega =  omega knot / ( 1 + (2mr^2/MR^2))

        omega (rim) = omega knot  M/ M+2m)

       Energy not conserved

Please reply with explanation..