Please wait...
Contact Us
Contact
Need assistance? Contact us on below numbers

For Study plan details

10:00 AM to 7:00 PM IST all days.

For Franchisee Enquiry

OR

or

Thanks, You will receive a call shortly.
Customer Support

You are very important to us

For any content/service related issues please contact on this number

9321924448

Mon to Sat - 10 AM to 7 PM

A bullet of mass M moving with velocity U just grazes the top of a solid cylinder of mass M and radius R resting on a rough horizontal surface .If the cylinder rolls without slipping then find the angular velocity of cylinder and the final velocity of the bullet

Asked by mvenkataram 22nd August 2019, 8:01 AM
Answered by Expert
Answer:
when the bullet which is moving initially with velocity v, just grazes the cylinder ,
contact point on the cylinder starts moving with velocity v.
 
We know that  if cylinder is rolling on rough horizontal surface without slipping and
the top most point moves with linear speed v , then centre of mass moves with speed v/2
and point of contact of cylinder with horizontal surface has zero velocity.
 
angular speed of cylinder = ω = v/(2R)  , where R is radius of cylinder
 
Initial kinetic energy Ei of bullet is given by,   Ei  = (1/2)Mv2 ..................................(1)
 
where M is mass of bullet
 
Kinetic energy EC of rolling cylinder is given by,   EC = (1/2)M(v/2)2 + (1/2)Iω2 .......................(2)
 
where M is mass of cylinder, I is moment of inertia
 
with substitution of I = MR2/2,  eqn.(2) is simplified  as,  EC = (3/16)Mv2 ....................(3)
 
Hence kinetic energy of bullet after grazing the cylinder, 
 
Ei - EC = (1/2)Mvf2 = (1/2)Mv2 - (3/16)Mv2 = (5/16)Mv2...................(4)
 
where vf is the bullet velocity after grazing the cylinder and it is obtained from eqn.(4) as, 
 
vf = 0.56 v
Answered by Expert 23rd August 2019, 10:17 AM
Rate this answer
  • 1
  • 2
  • 3
  • 4
  • 5
  • 6
  • 7
  • 8
  • 9
  • 10

You have rated this answer /10

Your answer has been posted successfully!

Chat with us on WhatsApp