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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

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

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

Velocity of the bob at the point A
$v equals square root of 5 g L end root$ (i)
$open parentheses fraction numerator v over denominator 2 end fraction close parentheses to the power of 2 end exponent equals v to the power of 2 end exponent minus 2 g h open parentheses i i close parentheses$
$h equals L left parenthesis 1 minus cos invisible function application theta right parenthesis left parenthesis i i i right parenthesis$
$S o l v i n g blank E q s. open parentheses i close parentheses comma blank open parentheses i i close parentheses a n d blank open parentheses i i i close parentheses comma blank w e blank g e t$
$cos invisible function application theta equals negative fraction numerator 7 over denominator 8 end fraction$
$o r blank theta equals c o s to the power of negative 1 end exponent open parentheses negative fraction numerator 7 over denominator 8 end fraction close parentheses equals 151 degree$

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