A particle of mass \(\mathrm{m}\) is projected at a velocity \(\mathrm{u}\), making an angle \(\theta\) with the horizontal ( \(\mathrm{x}\)-axis). If the angle of projection \(\theta\) is varied keeping all other parameters same, then magnitude of angular momentum (L) at its maximum height about the point of projection varies with \(\theta\) as,

• A

  
  
• B

  
  
• C

  
  
• Correct answer
  D

  
  

Solution

Hint :
\(\begin{aligned} & \mathrm{L}_0=m u \cos \theta \mathrm{H} \\ & =m u \cos \theta \frac{\mathrm{u}^2 \sin ^2 \theta}{2 \mathrm{~g}} \\ & =\frac{m u^3 \sin ^2 \theta \cos \theta}{2 \mathrm{~g}} \end{aligned}\) \(L\) is zero for \(\theta=0^{\circ}\) and \(\theta=\frac{\pi}{2}\)

Hence, the correct answer is option: 'D'.