Use app×
Join Bloom Tuition
One on One Online Tuition
JEE MAIN 2025 Foundation Course
NEET 2025 Foundation Course
CLASS 12 FOUNDATION COURSE
CLASS 10 FOUNDATION COURSE
CLASS 9 FOUNDATION COURSE
CLASS 8 FOUNDATION COURSE
0 votes
90 views
in Physics by (67.6k points)
closed by
A uniform rod of mas m and length l is kept vertical with the lower end clamed. It is slightly pushed to let it fall down under gravity. Find its angular speed when the rod is passing through its lowest positon. Neglect any friction at the clamp. What will be the linear speed of the free end at this instant?

1 Answer

0 votes
by (75.1k points)
selected by
 
Best answer

image
As the rod reaches its lowest position, the centre of mass is lowered by a distance l. Its gravitatioN/Al potential energy is decreased by mgl. As no energy lost against friction, this should be equal to the increase in the kinetic energy. As the rotation ocfurs about the horiztonsal axis through the clamped end, the moment of inertia is `I=ml^2/3`. Thus
`1/2Iomega^2=mgl`
`1/2((ml^2)/3)omega^2=mgl`
`or, omega sqrt(6g)/l`
the linear speed of the free end is
`v=lometa=sqrt(6gl)`

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.

Categories

...