question_answer 67)

                  The bob A of a pendulum released from horizontal to the vertical hits another bob B of the same mass at rest on a table as shown in Fig.                 If the length of the pendulum is 1m, calculate                 (a) the height to which bob A will rise after collision.                 (b) the speed with which bob B starts moving. Neglect die size of the bobs and assume die collision to be elastic.                

Answer:

                  (a) During elastic collision, bodies of equal masses interchange their velocities after collision.                 Since bob A has certain velocity (say \[\upsilon \]) and the bob B is at rest (i.e. \[\upsilon =0\]), so after collision, bob B will move with velocity v and bob A will come to rest. Hence, the bob will not rise at all.                 (b) Velocity of the bob A when it falls through a height h of h of  \[1\,m,\,\upsilon =\sqrt{2gh}\]                 \[=\,\sqrt{2\times 10\times 1}\]                 \[=\,\sqrt{20}=\,4.47\,\,m\,{{s}^{-1}}\]                 Thus, the bob will start moving with a speed of \[4.47\,\,m{{s}^{-1}}\].