Two uniform thin rods A and B of length 0.6m each and masses 0.01kg and 0.02kg respective are rigidly joined and to end. The combination is pivoted at the lighter end P as shown in fig. such that it c

Question

Two uniform thin rods A and B of length 0.6m each and masses 0.01kg and 0.02kg respective are rigidly joined and to end. The combination is pivoted at the lighter end P as shown in fig. such that it can freely rotate about the point P in a vertical plane. A small object of mass 0.05kg moving horizontally hits the lower end of the combination and sticks to it. What should be the speed of the object (in m/s) so that the system could just be raised to the horizontal position?

TestHub · Accepted Answer

Angular momentum about the hinge P during the impact (object sticks at the lower end, 1.2 m from P ): 0.05 × v × 1.2 = I ω , with I = 3 0.01 ( 0.6 ) 2 ​ + [ 12 0.02 ( 0.6 ) 2 ​ + 0.02 ( 0.9 ) 2 ] + 0.05 ( 1.2 ) 2 = 0.09 kg m 2 ⇒ ω = 3 2 v ​ . To just reach the horizontal position: 2 1 ​ I ω 2 = g [ 0.01 ( 0.3 ) + 0.02 ( 0.9 ) + 0.05 ( 1.2 )] = 0.81 J. 0.02 v 2 = 0.81 ⇒ v = 6.36 m/s.

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