A bob of heavy mass m is suspended by a light string of length l. The bob is given a horizontal velocity v _0 as shown in figure. If the string gets slack at some point P making an angle from the horizontal, the ratio of the speed v of the bob at point P to its initial speed v_0 is :
D. ( 2+3 )^ 1 2
C.O.M.E. 1 2 mv _0^2= mg (1+ )+ 1 2 mv _ p ^2....(1) At pt P Tp + mg = mv _ p ^2 ( as T _ p =0 ) mg = mv _ p ^2 mv _ p ^2= mg .( ii ) From (i) & (ii) aligned & 1 2 m v_0^2=m g (1+ )+ 1 2 m g \\ & v_0^2=2 g (1+ )+g \\ & v_0= 2 g +3 g ....(iii) aligned aligned & v _ p = g \\ & v _0= 2 ~g +3 ~g \\ & v _ p v _0 = 2+3 aligned
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