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Physics-

General

Easy

Question

Average torque on a projectile of mass $m$ , initial speed $u$ and angles of projection $theta$ , between initial and final position $P$ and $Q$ as shown in figure about the point of projection is

$m u^{2} \sin θ$
$m u^{2} \cos θ$
$\frac{1}{2} m u^{2} \sin 2 θ$
$\frac{1}{2} m u^{2} \cos 2 θ$

The correct answer is: $fraction numerator 1 over denominator 2 end fraction blank m u to the power of 2 end exponent sin invisible function application 2 theta$

Time of flight. $T equals fraction numerator 2 u sin invisible function application theta over denominator g end fraction$
Horizontal range, $R equals fraction numerator u to the power of 2 end exponent sin invisible function application 2 theta over denominator g end fraction$
Change in angular momentum,
$open vertical bar d stack L with rightwards arrow on top close vertical bar equals open vertical bar stack L with rightwards arrow on top subscript f end subscript minus stack L with rightwards arrow on top subscript i end subscript close vertical bar$ about point of projection
$equals left parenthesis m u sin invisible function application theta right parenthesis cross times fraction numerator u to the power of 2 end exponent sin invisible function application 2 theta over denominator g end fraction$
$equals fraction numerator m u to the power of 3 end exponent sin invisible function application theta sin invisible function application 2 theta over denominator g end fraction$
$T o r q u e blank open vertical bar stack tau with rightwards arrow on top close vertical bar equals fraction numerator c h a n g e blank i n blank a n g u l a r blank m o m e n t u m over denominator t i m e blank o f blank f l i g h t end fraction$
$equals open vertical bar fraction numerator d stack L with rightwards arrow on top over denominator T end fraction close vertical bar$

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