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One end of a light string of length `L` is connected to a ball and the other end is connected to a fixed point `O`. The ball is released from a rest at `t=0` with string horizontal and just taut. The ball then moves invertical circular path as shown. The time taken by ball to go from position `A` to `B` is `t_(1)` and from `B` to lowest position `B` to lowest position `C` is `t_(2)`. Let the velocity of ball at `B` is `vec(v)_(B)` and `C` is `vec(v)_(C)` respectively. If `|vec(v)_(C)|=|vec(v)_(B)|` then the value of `theta ` as shown isA. `cos^(-1) (1)/(4)`B. `sin^(-1) (1)/(4)`C. `cos^(-1) (1)/(2)`D. `sin^(-1) (1)/(2)` |
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Answer» Correct Answer - B `V_(B)=sqrt(2gLsintheta)` and `V_(C)=sqrt(2gL)` `V_(C)=2V_(B)` Then `2gL=4(2gL sin theta )` or `sin theta =(1)/(4) ` or `theta=sin ^(-1)((1)/(4))` |
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