Home
Class 11
PHYSICS
A uniform thin circular ring of mass m (...

A uniform thin circular ring of mass `m (m = 0.4 kg)` and radius `R` has a small particle of the same mass m fixed on it as shown in Fig. The line joining the particle to centre is initially horizontal. The ground is frictionless. Find the contact force (magnitude) exerted by the ground on the ring, when the system is released from rest.

Text Solution

Verified by Experts

The correct Answer is:
`3/2mg`
Applying torque equation about centre of mas
`tau_(CM)=I_(CM)alpha`………i
`implies N R/2=(I_(CM))alpha`…ii
`I_(CM)=mR^(2)+m(R/2)^(2)+m(R/2)^(2)=3/2mR^(2)`
The `CM` of system (ring+particle) will be at a distance `R//2` from the centre of the ring.

`2mg-N=2m(a_(CM))_(y)` .....iii
using constraint acceleration of centre of circle is zero
`(a_c)_(y)=0`
`implies R/2alpha=(a_(CM)_(y))`.......iv
Form ii, iii and iv we get
`N=3/2mg`
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • RIGID BODY DYNAMICS 2

    CENGAGE PHYSICS ENGLISH|Exercise Single Correct|142 Videos

  • RIGID BODY DYNAMICS 2

    CENGAGE PHYSICS ENGLISH|Exercise Multiple Correct|26 Videos

  • RIGID BODY DYNAMICS 2

    CENGAGE PHYSICS ENGLISH|Exercise Exercise 3.4|13 Videos

  • RIGID BODY DYNAMICS 1

    CENGAGE PHYSICS ENGLISH|Exercise Integer|11 Videos

  • SOUND WAVES AND DOPPLER EFFECT

    CENGAGE PHYSICS ENGLISH|Exercise Integer|16 Videos

Similar Questions

Explore conceptually related problems

A thin spherical shell of mass M and radius R has a small hole. A particle of mass m released at its mouth. Then

A uniform ring of mass m and radius 3a is kept above a sphere of mass M and radius 3a at a distance of 4a (as shown in figure) such that line joining the centres of ring and sphere is perpendicular to the plane of the ring. Find the force of gravitational attraction between the ring and the sphere.

Knowledge Check

  • A uniform ring of mas m and radius a is placed directly above a uniform sphere of mass M and of equal radius. The centre of the ring is at a distance sqrt3 a from the centre of the sphere. Find the gravitational force exerted by the sphere on the ring.

    A
    `(GMm)/(8r^(2))`
    B
    `(GMm)/(4r^(2))`
    C
    `sqrt(3)(GMm)/(8r^(2))`
    D
    `(GMm)/(8r^(3)sqrt(3))`

    • Similar Questions

    Explore conceptually related problems

    A circular ring of mass M and radius 'a' is placed in a gravity free space. A small particle of mass m placed on the axis of the ring at a distance sqrt(3)a from the center of the ring, is released from rest. The velocity with which the particle passes through the center of the ring is

    A ring mass m and radius R has three particle attached to the ring as shown in the figure. The centre of the centre v_(0) . Find the kinetic energy of the system. (Slipping is absent). .

    A uniform ring of mas m and radius a is placed directly above a uniform sphere of mass M and of equal radius. The centre of the ring is at a distance sqrt3 a from the centre of the sphere. Find the gravitational force exerted by the sphere on the ring.

    A circular ring of mass m and radius R rests flat on a horizontal smooth surface as shown in figure. A particle of mass m , and moving with a velocity v . Collides inelastically (e=0) with the ring the angular velocity with which the system rotates after the particle strikes the ring is

    A uniform ring of mas m and radius a is placed directly above a uniform sphere of mass M and of equal radius. The center of the ring is at a distance sqrt3 a from the center of the sphere. Find the gravitational force exerted by the sphere on the ring.

    A solid sphere of mass m and radius r is placed inside a hollow thin spherical shell of mass M and radius R as shown in the figure. A particle of mass m' is placed on the line joining the two centres at a distance x from the point of contact of the sphere and the shell. Find the magnitude of the resultant gravitational force on this particle due to the sphere and the shell if rltxlt2r

    A solid sphere of mass m and radius r is placed inside a hollow thin spherical shell of mass M and radius R as shown in the figure. A particle of mass m' is placed on the line joining the two centres at a distance x from the point of contact of the sphere and the shell. Find the magnitude of the resultant gravitational force on this particle due to the sphere and the shell if xgt2R

    Home
    Profile