A simple pendulum is oscillating with an angular amplitude of 90o as shown in fig. (4). The value of θ forwhich the resultant acceleration of the bob is directed horizontally is

See fig. (11).From figure     at=gsin⁡θand    ac=v2l=2glcos⁡θl=2gcos⁡θNow,    tan⁡θ=acsin⁡90∘at+accos⁡90∘or       tan⁡θ=2gcos⁡θgsin⁡θ=2tan⁡θor      tan2⁡θ=2  or  sec2⁡θ=3∴ cos⁡θ=1/3θ=cos−1⁡(1/3)