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Physics-

General

Easy

Question

A bob of mass $M$ is suspended by a massless string of length $L$ . The horizontal velocity $V$ at position $A$ is just sufficient to make it reach the point $B$ . The angle $theta$ at which the speed of the bob is half of that at $A$ , satisfies

$θ = \frac{π}{4}$
$\frac{π}{4} < θ < \frac{π}{4}$
$\frac{π}{2} < θ < \frac{3 π}{4}$
$\frac{3 π}{4} < θ < π$

The correct answer is: $fraction numerator 3 pi over denominator 4 end fraction less than theta less than pi$

$V to the power of 2 end exponent equals U to the power of 2 end exponent minus 2 g left parenthesis L minus L cos invisible function application theta right parenthesis$
$fraction numerator 5 g L over denominator 4 end fraction equals 5 g L minus 2 g L left parenthesis 1 minus cos invisible function application theta right parenthesis$

$5 equals 20 minus 8 plus 8 cos invisible function application theta$
$cos invisible function application theta equals negative fraction numerator 7 over denominator 8 end fraction$
$fraction numerator 3 pi over denominator 4 end fraction less than theta less than pi$

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