A ring of mass `M` and radius `R` lies in `x-y` plane with its centre at origin as shown. The mass distribution of ring is non uniform such that, at any point `P` on the ring, the mass per unit length is given by `lamda = lamda_0 cos^2 theta` (where `lamda_0` is a positive constant). Then the moment of inertia of the ring about z-axis is : .A. `MR^2`B. `(1)/(2) MR^2`C. `(1)/(2) (M)/(lamda_0) R`D. `(1)/(pi) (M)/(lamda_0) R`

A ring of mass `M` and radius `R` lies in `x-y` plane with its centre

1.	A ring of mass `M` and radius `R` lies in `x-y` plane with its centre at origin as shown. The mass distribution of ring is non uniform such that, at any point `P` on the ring, the mass per unit length is given by `lamda = lamda_0 cos^2 theta` (where `lamda_0` is a positive constant). Then the moment of inertia of the ring about z-axis is : .A. `MR^2`B. `(1)/(2) MR^2`C. `(1)/(2) (M)/(lamda_0) R`D. `(1)/(pi) (M)/(lamda_0) R`
Answer» Correct Answer - A (a) Divide the ring into infinitely small lengths of mass `dm_i`. Even through mass distribution is non-uniform, each mass `dm_i` is at same distance `R` from origin. :. `MI` of ring about z-axis is =`dm_ R^2 + dm_2 R^2 + …+ dm_n R^2 = MR^2`.

Discussion

No Comment Found

Related InterviewSolutions

A tight rope walker in a circus holds a long flexible pole to help stay balanced on the rope. Honding the pole horizontally and perpendicular to the rope helds the performer. .A. by lowering the overall centre of gravityB. by increasing the rotation inertiaC. in the ability to adust the centre gravity to the be over the ropeD. in achieving the centre of gravity to be under the rope.
A sphere of mass `M` and radius `R` is attached by a light of length `1` to a point `P`. The sphere rolls without slipping on a circular track as shown. It is released from the horizontal position. The angular momentum of the system about `P` when the rod becomes vertical is : .A. `M sqrt((10)/(7)) gl[l + R]`B. `M sqrt((10)/(7)) gl[ l + (2)/(5) R]`C. `M sqrt((10)/(7)) gl [l +(7)/(5) R]`D. none of the above
A solid sphere rolling on a rough horizontal surface. Acceleration of contact point is zero. A solid sphere can roll on the smooth surface.A. If both assertion and reason are true and reason is the true explanation of assertion.B. If both assertion and reason are reason are true but reason is not the correct explanation of assertion.C. If assertion is true but reason is falseD. If both assertion and reason are false.
A sphere is performing pure rolling on a rough horizontal surface with constant angular velocity. Frictional force acting on the sphere is zero. Velocity of contact point is zero.A. If both assertion and reason are true and reason is the correct explanation of assertion.B. If both assertion and reason are reason are true but reason is not the correct explanation of assertion.C. If assertion is true but reason is falseD. If both assertion and reason are false.
A sphere is performing pure rolling on a rough horizontal surface with constant angular velocity. Frictional force acting on the sphere is zero. Velocity of contact point is zero.A. Statement-1 is True, Statement-2 is Ture , Statement -2 is a correct explanation for statement -1.B. Statement-1 is True, Statement-2 is True , Statement-2 is NOT a correct explanation fro Statement -1.C. Statement-1 is True, Statement-2 is False.D. Statement-1 is False, Statement-2 is True.
A mass M moving with a constant velocity parlale to the X-axis. Its angular momentum with respect to the originA. is zeroB. remains constantC. goes on increasingD. goes on decreasing
A solid sphere is rotating in free space. If the radius of the sphere is increased keeping mass same which one of the following wil not be affected?A. Moment of inertiaB. Angular momentumC. Angular velocityD. Rotational kinetic energy
A circular platform is mounted on a vertical frictionless axle. Its radius is `r = 2 m` and its moment of inertia`I = 200 kg m^2`. It is initially at rest. A `70 kg` man stands on the edge of the platform and begins to walk along the edge at speed `v_0 = 1 m s^-1` relative to the ground. The angular velocity of the platform is.A. `1.2 rad s^-1`B. `0.4 rad s^-1`C. `0.7 rad s^-1`D. `2 rad s^-1`
A ring of radius `R` is rotating with an angular speed `omega_0` about a horizontal axis. It is placed on a rough horizontal table. The coefficient of kinetic friction is `mu_k`. The time after it starts rolling is.A. `(omega_0 mu_k R)/(2 g)`B. `(omega_0 g)/(2 mu_k R)`C. `(2 omega_0 R)/(mu_k g)`D. `(omega_0 R)/(2 mu_k g)`]
Two bodies `A and B` initially at rest are attrached towards each other due to gravitation. Given that `A` is much heavier. Than `B`. Which of the followings correctly describes the relative motion of the centre of mass of the bodies ?A. it moves towards `A`B. it moves towards `B`C. it moves perpendicular to the line joining the particlesD. it remains at rest.

Discussion

No Comment Found

Related InterviewSolutions

Reply to Comment