Home
Class 11
PHYSICS
A smooth chain (AB) of mass (m) rests ag...

A smooth chain (AB) of mass (m) rests against a surface in the form of a quarter of circle of radius R. If it is released from rest, the form of a quarter of a circle of radius R. If it is releaded from, the velocity of the chain after it comes over the horizontal part of the surface is .

A

(a) `sqrt2gR`

B

(b) `sqrt(gR)`

C

(c) `sqrt(2gR(1-(2)/(pi)))`

D

(d) `sqrt(2gR(2-pi))`

Text Solution

Verified by Experts

The correct Answer is:
C
`dm((m)/(pi//(2)) dtheta = (((2m)/(pi))) d theta`
`h = R(1 - costheta)`

`dU_(i) =(dm) gh=(2mgR)/(pi)(1-cos theta) d theta`
`:. U_(i) =int_(0)^(pi//2)dU_(i) =(2mgR)/(pi)((pi)/(2) -1)`
`:. =mgR(1-(2)/(pi))`
Now, `U_(i) + K_(i) =U_(f) K_(f)`
`:. mgR(1-(2)/(pi)) =0 +1/2mv^(2)`
or `v=sqrt(2gR(1-(2)/(pi)))`
Promotional Banner

Similar Questions

Explore conceptually related problems

A chain AB of length equal to the quarter of a circle of radius R is placed on a smooth hemisphere as shown in figure -3.66. When it is released, it starts falling. Find the velocity of the chain when it falls of the end B from the hemisphere.

A particle moves over three quarters of a circle of radius r . What is the magnitude of its displacement ?

A particle moves over three quarters of a circle of radius r . What is the magnitude of its displacement ?

A particle of mass m is released from the top of a smooth hemisphere of radius R with the horizontal speed mu . Calculate the angle with verticle where it loses contact with the hemisphere.

A block of mass M with a semi - circular track of radius R rests on a smooth floor. A sphere of mass m and radius r is released from rest from A . Find the velocity of sphere and track , when the sphere reaches B .

A ball of mass m and radius r rolls inside a fixed hemispherical shell of radius R . It is released from rest from point A as shown in figure. The angular velocity of centre of the ball in position B about the centre of the shell is. .

A roadway bridge over a rivulet is in the form of quarter of a circle of radius 60 m. What is the maximum speed with which a car can pass over the bridge without leaving the ground at any point ?

A small bead of mass M slides on a smooth wire that is bent in a circle of radius R. It is released at the top of the circular part of the wire (point A in the figure) with a negligibly small velocity. Find the height H where the bead will reverse direction

Starting from rest, a particle rotates in a circle of radius R  2 m with an angular acceleration  = /4 rad/s2.The magnitude of average velocity of the particle over the time it rotates quarter circle is:

A uniform chain of length 1 and mass m is kept on a smooth table. It is released from rest when the overhaning part was n^(th) fraction of total length. Find the kinetic energy of the chain as it completely slips off the table