(See the image on -- http://www.flickr.com/photos/58839342@N00/101683085/ [Broken] ) 1.) A ring of mass m and radius R is placed on a smooth horizontal surface. A small ball of same mass is given a velocity v/(sqrt2) from a point A (towards B) close to inner surface of the ring at 45 degrees from the line AO. If all the collisions are assumed elastic, then what is the time after which the ball will return to it's original position with respect to ring. After the first collision the ring and ball interchange velocities. Time taken till the first collision takes place is 2R/v. After this collison relative velocity reverses it's direction. So time taken is 4R/v. (But ans is 8R/v) 2.) Two hollow concentric conducting shells of radii a and 4a are shown. The outer shell is connected with a battery of Potential Difference 3V and the inner shell is earthed. What is the electrostatic energy of the system? p = pi e = epsilon (8.85 * 10^-12) The capacitance of system is [(4 p e r1 r2)/(r1-r2)] in this case r1 is 4a and r2 is a so the capacitance is 16pea/3. energy is 1/2 CV^2. Putting V= 3 and capacitance i get 24pea. (Ans is 96pea) 3.)An organ pipe of lenght l is sounded together with another organ pipe of length l+x in their fundamental overtones (x<<l). What is the beat frequency heard? (speed of sound in air = v) There is nothing given whether the pipe is closed or open. So I assumed them to be closed and got vx/(2l)^2. However the right answer is through an open organ pipe (vx/2l^2). Should it be mentioned that we have to take open or closed or it must be obvious? Any help?