badge image

Enroll For Free Now & Improve Your Performance.

×
User Icon
User Icon
User Icon
User Icon
User Icon

Thank you for registering.

One of our academic counsellors will contact you within 1 working day.

Please check your email for login details.
MY CART (5)

Use Coupon: CART20 and get 20% off on all online Study Material

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: Rs.

There are no items in this cart.
Continue Shopping
Menu
Grade: 12th pass

                        

A particle is hanging from a fixed point O by means of a string of length a.there is a small nail Q in the same horizontal line with O at a distance between(b=a/3) from O.find the minimum velocity with which the particle should be projected so that it may make a complete revolution around the nail without being slackened.

2 years ago

Answers : (1)

Arun
24742 Points
							
Dear student
 
 
Here we have to find the velocity of particle at the lowest position required to complete the constrained motion arround the nail
Firstly we know that the velocity required to complete 90° is sqrt(2ga) 
Total kinetic energy decrease to complete 90 of the circle of radius a K1 = 1/2mv
now the radius of particle is decreased to 2a/3 
so , we know that the velocity required to complete a circle with radius R is /{sqrt{5gr}}
so here R =2a/3  v at
Lets take it as a completely rotational motion about point O and Q.
by energy conservation(wb representa angular velocity at the bottom (ZPL) and wT represents the velocity at the top)
(1/2)I1wb= mg(a+2a/3) + (1/2)I2wT2  ...(1)
Simplify it to get  
(1/2)(ma2)wb= mg(a+2a/3) + (1/2)(m(2a/3)2)wT
put values I= ma2 ; I=m(2a/3)2 .
here we need to find wb , so we will eleminate w:
at the top the Tension just tends to 0
Therefore, mwT2(2a/3) = mg
Now, substitute the value of mwT(2a/3) in equation 1 :
(1/2)(ma2)wb= mg(5a/3)+(1/2)(mg(2a/3))
Solve this to get :
Wb=2{\sqrt{g/a}}
So the velocity at bottom will be 
Vb = 2{\sqrt{ga}}
2 years ago
Think You Can Provide A Better Answer ?
Answer & Earn Cool Goodies


Course Features

  • 101 Video Lectures
  • Revision Notes
  • Previous Year Papers
  • Mind Map
  • Study Planner
  • NCERT Solutions
  • Discussion Forum
  • Test paper with Video Solution


Course Features

  • 110 Video Lectures
  • Revision Notes
  • Test paper with Video Solution
  • Mind Map
  • Study Planner
  • NCERT Solutions
  • Discussion Forum
  • Previous Year Exam Questions


Ask Experts

Have any Question? Ask Experts

Post Question

 
 
Answer ‘n’ Earn
Attractive Gift
Vouchers
To Win!!! Click Here for details