A particle o frnass m' moves in horizontal plane along the curve s= a0 as shown in figure, where o is angle made by tangent to the curve with x-axis ands is the distance coverved along the curve. Lagrangian of particle is : 41. y (b) m sin² nn (0) –ma² cos² né² (d) mu² sin² o6² 42. In previous question if equation of path of the particle be s= 4a sino then its lagrangian is: (a) 4ma²ô² (1+ cos 20) (b) 4ma²o* (1-cos 20) (e) 2ma-o* (1+ cos 20) (d) 8ma 0 cos e

A particle o frnass m' moves in horizontal plane along the curve s= a0 as shown in figure, where o is angle made by tangent to the curve with x-axis ands is the distance coverved along the curve. Lagrangian of particle is : 41. y (b) m sin² nn (0) –ma² cos² né² (d) mu² sin² o6² 42. In previous question if equation of path of the particle be s= 4a sino then its lagrangian is: (a) 4ma²ô² (1+ cos 20) (b) 4ma²o* (1-cos 20) (e) 2ma-o* (1+ cos 20) (d) 8ma 0 cos e

Classical Dynamics of Particles and Systems

5th Edition

ISBN:9780534408961

Author:Stephen T. Thornton, Jerry B. Marion

Publisher:Stephen T. Thornton, Jerry B. Marion

Chapter4: Nonlinear Oscillations And Chaos

Section: Chapter Questions

Problem 4.21P

See similar textbooks

Similar questions

The arc length formula says the length sof arc subtended by angle in a circle of radius r is given by the equation s=r . What are the dimensions of (a) s, (b) r , and (c) ?
Consider the physical quantities s,v,a, and t with dimensions [s]=L,[v]=LT1,[a]=LT2 and [t]=L . Determine whether each of the following equations is dimensionally consistent. (a)v2=2as;(b)s=vt2+0.5at2;(c)v=s/t;(d)a=v/t
Consider the equation s=s0+v0t+a0t2/2+j0t3/6+s0t4/24+ct5/120 , were s is a length and t is a time. What are the dimensions and SI units of (a) s0 , (b) v0 , (c) a0 , (d) j0 , (e) s0, and (f) c ?
Obtain the sine law of plane trigonometry by interpreting the product A × B and the alternate representation (A − B) × B.
Show that when 1(x,t) and 2(x,t) are solutions to the time-dependent Schrödinger equation and A, B are numbers then a function (x,t) that is a superposition of these functions is also a solution: (x,t)=A1(x,t)+B1(x,t).
Rectangular coordinates of a point are given by (2,y) and its polar coordinates are given by (r,/6) . Find y y and r .
Explain why, when defining the length of a rod, it is necessary to specify that the positions of the ends of the rod are to be measured simultaneously.
A marathon runner completes a 42.188-km course in 2 h, 30 min, and 12s. There is an uncertainty of 25 m in the distance traveled and an uncertainty of 1 s in the elapsed time. (a) Calculate the percent uncertainty in the distance. (b) Calculate the percent uncertainty in the elapsed time. (C) What is the average speed in meters per second? (d) What is the uncertainty in the average speed?
The length and width of a rectangular room are measured to be 3.9550.005m and 10500.005m . Calculate the area of the room and its uncertainty in square mete
The first atomic bomb was detonated on July 16, 1945, at the Trinity test site about 200 mi south of Los Alamos. In 1947, the U.S. government declassified a film reel of the explosion. From this film reel, British physicist G.I. Taylor was able to determine the rate at which the radius of the fireball from the blast grew. Using dimensional analysis, he was then able to deduce the amount of energy released in the explosion, which was a closely guarded secret at the time. Because of this, Taylor did not publish his results until 1950. This problem challenges you to recreate this famous calculation. (a) Using keen physical insight developed from years of experience, Taylor decided the radius rof the fireball should depend only on time since the explosion, t, the density of the air, , and the energy of the initial explosion, E. Thus, he made the educated guess that r=kEabtcfor some dimensionless constant kand some unknown exponents a,b, and c. Given that [E]=ML2T-2 , determine the values of the exponents necessary to make this equation dimensionally consistent. (Hint: Notice the equation implies that k=rEabtcand that [k]=1 ). (b) By analyzing data from high-energy conventional explosives, Taylor found the formula he derived seemed to be valid as long as the constant khad the value 1.03. From the film reel, he was able to determine many values of rand the corresponding values of t. For example, he found that after 25.0 ms, the fireball had a radius of 130.0 m. Use these values, along with an average air density of 1.25kg/m3 , to calculate the initial energy release of the Trinity detonation in joules (J). (Hint: To get energy in joules, you need to make sure all the numbers you substitute in are expressed in terms of SI base units.) (c) The energy released in large explosions is often cited in units of “tons of TNT” (abbreviated “t TNT”), where 1 t TNT is about 4.2 GJ. Convert yow answer to (b) into kilotons of TNT (that is, kt TNT). Compare your answer with the quick-and-duty estimate of 10 kt TNT made by physicist Enrico Fermi shortly after witnessing the explosion from what was thought to be a safe distance. (Reportedly, Fermi made his estimate by dropping some shredded bits of paper right before the remnants of the shock wave hit him and looked to see how far they were carried by it.)
What is wrong with the following expressions? How can you correct them? (a) C=AB , (b) C=AB , (c) C=AB , (d) C=AB , (e) C+2A=B , (f) C=AB , (g) AB=AB , (h) C=2AB , (i) C=A/B , and (j) C=A/B .
Explain the difference between time-dependent and independent SchrÖdinger's equations.