Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Medical
  • A rod of uniform mass density XY of mass '' and length <img alt="l" src="https://entrancecorner.oncodecogs.com/gi

A rod of uniform mass density XY of mass 'm' and length l leans with its lower end against the wall. A string connects the rod with the wall such that XZ=\frac{X Y}{4}. The angles made by the string and the rod with the wall are \theta and \phi respectively. Assuming. the force of friction to be zero. The correct relationship between \theta and \phi will be -

Option: 1

2 \tan \theta =\tan \phi


Option: 2

\tan \theta =2\tan \phi


Option: 3

\tan \theta =\tan \phi


Option: 4

2 \tan \theta =3\tan \phi


Answers (1)

As the rod is in equilibrium, the sum of torque about any point should be zero.

Three forces tension,(T), mg and normal reaction, intersects at point P shown in the figure.

\begin{array}{r} T \cos \theta-m g=0 \\ N-T \sin \theta=0 \end{array}

Taking torque about point 'X'

m g\left(\frac{l}{2}\right) \sin \phi=T\left(\frac{l}{4}\right) \sin (\theta+\phi) \\

       {m g \sin \phi}=\frac{{T}}{2} \cdot \sin (\theta+\phi) \\

________________________________________

                mg=T cos\theta

     \begin{aligned} & \sin \phi=\frac{\sin (\theta+\phi)}{2 \cos \theta} \\ & 2 \sin \phi \cdot \cos \theta=\sin \theta \cdot \cos \phi+\cos \theta \cdot \sin \phi \\ & \sin \theta \cdot \cos \phi=\cos \theta \cdot \sin \phi \\ & \tan \theta=\tan \phi \end{aligned}

Posted by

Sumit Saini

View full answer

NEET 2024 Most scoring concepts

    Just Study 32% of the NEET syllabus and Score up to 100% marks

Similar Questions

Trending Articles/News

anam-khan

Abolish NEET, restore state CET; Karnataka urges Centre after paper leak row
anam-khan

NEET UG 'Leak': CBI probing role of NTA-linked public servant
anam-khan

NEET Paper Leak: Siddaramaiah backs Rahul Gandhi; seeks Dharmendra Pradhan’s removal

Latest Question