JEE Class main Answered
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 | 22 Aug, 2019, 08:01: AM
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 Thiyagarajan K | 23 Aug, 2019, 10:17: AM
Application Videos
Concept Videos
JEE main - Physics
Asked by sumalathamadarapu9 | 23 Oct, 2024, 22:06: PM
ANSWERED BY EXPERT
JEE main - Physics
Asked by py309649 | 13 Oct, 2024, 13:39: PM
ANSWERED BY EXPERT
JEE main - Physics
Asked by coolskrish | 13 Oct, 2024, 12:50: PM
ANSWERED BY EXPERT
JEE main - Physics
Asked by midnightmoon3355 | 09 Oct, 2024, 09:09: AM
ANSWERED BY EXPERT
JEE main - Physics
Asked by rambabunaidu4455 | 03 Oct, 2024, 16:03: PM
ANSWERED BY EXPERT
JEE main - Physics
Asked by ratchanavalli07 | 17 Sep, 2024, 07:46: AM
ANSWERED BY EXPERT
JEE main - Physics
Asked by yayashvadutta45 | 15 Sep, 2024, 19:47: PM
ANSWERED BY EXPERT
JEE main - Physics
Asked by adithireddy999 | 03 Sep, 2024, 09:35: AM
ANSWERED BY EXPERT
JEE main - Physics
Asked by vaishalinirmal739 | 29 Aug, 2024, 18:07: PM
ANSWERED BY EXPERT
JEE main - Physics
Asked by vradhysyam | 26 Aug, 2024, 17:17: PM
ANSWERED BY EXPERT