Question

Question 11 A rectangular block, with face lengths a = 33.0 cm and b = 46.0 cm, is to be suspended on a thin horizontal rod running through a narrow hole in the block. The block is then to be set swinging about the rod like a pendulum, through small angles so that it is in SHM. The figure shows one possible position of the hole, at distance from the block's center, along a line connecting the center with a corner. (a) For what value of r does the minimum the period of the pendulum occur? There is actually a line of points around the block's center for which the period of swinging has the same minimum value. (b) What shape does that line make? (a) Number Units (b)

Answer 1

Solution: Given data a 33 cm b46cm I T- a) The period of the oscillation is 21 / Mgr - SI- 1 / M Ca²+62) + MY 2 is the rotational inertia of the block arou 1 here the rotational axis. ► divide both sides by 'mgr I + Ca? +62) 91 Mgr Mgr. og To minimize this differentiate on both sides wor.tr I Ca2+62) 1 12 . 2 a2+62 12 (33)² + 46² 12 (33)+ 46) => 0 min 12 - 40.03 cm 6) let the Co-ordinates of the point is cxiy) then x?ty? À (a+b) => constant. | x² + y² = x² k² - Then the shape is circular