Browse by Stream
Discuss Doubts
Home
Search for Exam, Articles, Questions
get app
Go To Your Study Dashboard
  1. Home
  2. a small particle of mass m is projected
# Engineering

Screenshot_2019-03-02-12-37-03-078_com.android.chrome.png

A small particle of mass m is projected at an angle \Theta with the  x-axis with an initial velocity \upsilon _{0} in the  x-y plane as shown in the figure. At a time t< \frac{\upsilon _{0}\sin \Theta }{g}, the angular momentum of the particle is

where \hat{i},\hat{j}\, and\, \hat{k} are unit vectors along x,y and z-axis respectively.

Answers (1)
S safeer

 \vec{v}_x = \left ({v_{0}} \right \cos \Theta)\hat{i}

\vec{v}_y = \left ( v_{0} \right\sin \Theta -gt )\hat{j}

\vec{v} ={v}_x\hat{i}\:+{v}_{y}\hat{j}

\vec{v} = v_{o}\cos \Theta \hat{i} + \left (v _{0} sin \Theta \right - gt )\hat{j}

\vec{r} = v_{o} \cos \Theta \hat{i} + \left (v_{o} \sin \Theta t- {\tfrac{1}{2}} gt^2 \right )\hat{j}

Angular momentum

= \vec{L} = m\left ( \vec{r} \times \right\vec{v} )

L = m (v_0cos\Theta \hat{i}+(v_0sin\Theta t-\frac{1}{2}gt^2)\vec{j})\times (v_0cos\Theta \hat{i}+(v_0sin\Theta-gt))\hat{j}

L = m [v^2_0cos\Theta sin\Theta t - v_0gt^2cos\Theta]\hat{k}+(v^2_0sin\Theta cos\Theta t - \frac{1}{2}gt^2v_0cos\Theta (-\hat{k})

L =m (v^2_0sin\Theta cos\Theta t \hat{k} - v_0gt^2 cos\Theta (\hat{k}) - v^2_0sin\Theta cos\Theta t \hat{k} +\frac{1}{2}mgv_0t^2cos\Theta \hat{k}

L =m[- \frac{1}{2}v_0gt^2cos\Theta \hat{k}]

L =\frac{1}{2}mgv_0t^2cos\Theta \hat{k}

Similar Questions

Preparation Products

Knockout JEE Main April 2021

An exhaustive E-learning program for the complete preparation of JEE Main..

₹ 22999/- ₹ 14999/-
Buy Now
Knockout JEE Main April 2022

An exhaustive E-learning program for the complete preparation of JEE Main..

₹ 34999/- ₹ 24999/-
Buy Now
Test Series JEE Main April 2021

Take chapter-wise, subject-wise and Complete syllabus mock tests and get in depth analysis of your test..

₹ 6999/- ₹ 4999/-
Buy Now
JEE Main Rank Booster 2021

This course will help student to be better prepared and study in the right direction for JEE Main..

₹ 13999/- ₹ 9999/-
Buy Now
Test Series JEE Main April 2022

Take chapter-wise, subject-wise and Complete syllabus mock tests and get an in-depth analysis of your test..

₹ 6999/-
Buy Now
Boost your Preparation for JEE Main 2021 with Personlized Coaching
Start Now
 
Exams
Articles
Questions