Physics
Mechanics
Easy

Question

A circular disc A of radius r is made from an iron plate of thickness t and another circular disc B of radius 4r and thickness t/4. The relation between moments of inertia IA and IB about the same axis is :

  1. I subscript A greater than I subscript B
  2. I subscript A equals I subscript B
  3. I subscript A less than I subscript B
  4. depends on the actual values of t and r

The correct answer is: I subscript A less than I subscript B


    m subscript A equals text volume end text cross times text density end text equals pi r squared t rho
    I subscript A equals 1 half m subscript A r squared equals 1 half pi r to the power of 4 rho t
    text Similarly   end text I subscript B equals 1 half pi left parenthesis 4 r right parenthesis to the power of 4 rho left parenthesis t over 4 right parenthesis equals 64 I subscript A
    text Clearly   end text I subscript B greater than I subscript A

    Related Questions to study

    Mechanics
    Physics

    A triangular plate of uniform thickness and density is made to rotate about an axis perpendicular to the plane of the paper and (i) passing through A, (ii) passing through B, by the application of some force F at C as shown in the figure. In which case angular acceleration is more ?

    A triangular plate of uniform thickness and density is made to rotate about an axis perpendicular to the plane of the paper and (i) passing through A, (ii) passing through B, by the application of some force F at C as shown in the figure. In which case angular acceleration is more ?

    PhysicsMechanics
    Mechanics
    Physics

    In  a  rectangle ABCD, AB =21 and BC=1. Axes x x and y y pass through centre of the rectangle . The moment of inertia is least about :

    In  a  rectangle ABCD, AB =21 and BC=1. Axes x x and y y pass through centre of the rectangle . The moment of inertia is least about :

    PhysicsMechanics
    Mechanics
    Physics

    Moment of inertia of uniform triangular plate about axis passing through sides AB,AC, BC are IP,IB and IH respectively and about an axis perpendicular to the plane and passing through point C is IC, then :

    Moment of inertia of uniform triangular plate about axis passing through sides AB,AC, BC are IP,IB and IH respectively and about an axis perpendicular to the plane and passing through point C is IC, then :

    PhysicsMechanics
    parallel
    Mechanics
    Physics

    Consider a uniform square plate of side a and mass m. The moment of inertia of this plate about an axis perpendicular to its plane and passing through one of its corners is

    Consider a uniform square plate of side a and mass m. The moment of inertia of this plate about an axis perpendicular to its plane and passing through one of its corners is

    PhysicsMechanics
    Mechanics
    Physics

    The moments of inertia of a thin square plate ABCD of uniform thickness about an axis posing through the centre 0 and perpendicular to the plate are

    (where /2, 1 and 14 are, respectively, the moments of inertia about axes I, 2, 3 and 4, where axes are in the plane of the plate)

    The moments of inertia of a thin square plate ABCD of uniform thickness about an axis posing through the centre 0 and perpendicular to the plate are

    (where /2, 1 and 14 are, respectively, the moments of inertia about axes I, 2, 3 and 4, where axes are in the plane of the plate)

    PhysicsMechanics
    Mechanics
    Physics

    Three point masses m,mand m3 am located at the vertices of an equilateral triangle of side 'a'. What is the moment of inertia of the system about an axis along the altitude of the triangle passing through m1 ?

    Three point masses m,mand m3 am located at the vertices of an equilateral triangle of side 'a'. What is the moment of inertia of the system about an axis along the altitude of the triangle passing through m1 ?

    PhysicsMechanics
    parallel
    Mechanics
    Physics

    A thin rod of length 4/ and mass 4m is bent at the points as shown in Fig. What is the moment of inertia of the rod about the axis passing through point O and perpendicular to the plane of the paper

    A thin rod of length 4/ and mass 4m is bent at the points as shown in Fig. What is the moment of inertia of the rod about the axis passing through point O and perpendicular to the plane of the paper

    PhysicsMechanics
    Mechanics
    Physics

    A smooth uniform rod of length L and mass M has two identical beads (1 and 2) of negligible size, each of mass m, which can slide freely along the rod. Initially the two beads are at the  centre of the rod and the system is rotating with angular velocity omega subscript a about an axis perpendicular to the rod and is passing through its midpoint. There are no external forces when the beads reach the ends of the rod, the angular velocity of the system is

    A smooth uniform rod of length L and mass M has two identical beads (1 and 2) of negligible size, each of mass m, which can slide freely along the rod. Initially the two beads are at the  centre of the rod and the system is rotating with angular velocity omega subscript a about an axis perpendicular to the rod and is passing through its midpoint. There are no external forces when the beads reach the ends of the rod, the angular velocity of the system is

    PhysicsMechanics
    Mechanics
    Physics

    The moment of inertia of an angular wheel shown in figure is 3200 kgm2. If the inner radius is 5 cm and the outer radius is 20cm, and the wheel is acted upon by the forces shown, then the angular acceleration of the wheel is

    The moment of inertia of an angular wheel shown in figure is 3200 kgm2. If the inner radius is 5 cm and the outer radius is 20cm, and the wheel is acted upon by the forces shown, then the angular acceleration of the wheel is

    PhysicsMechanics
    parallel
    Mechanics
    Physics

    A wheel of moment of inertia 2.0 cross times 10 cubed kgm squared is rotating at uniform angular speed of 4 rads to the power of negative 1 end exponent. What is the torque required to stop it in one second.

    A wheel of moment of inertia 2.0 cross times 10 cubed kgm squared is rotating at uniform angular speed of 4 rads to the power of negative 1 end exponent. What is the torque required to stop it in one second.

    PhysicsMechanics
    Mechanics
    Physics

    Let  be a force acting on a particle having position vector  . Let   be the torque of this force about the origin, then-

    Let  be a force acting on a particle having position vector  . Let   be the torque of this force about the origin, then-

    PhysicsMechanics
    Mechanics
    Physics

    The three similar torque (t) are acting at an angle of 120º with each other. The resultant torque will be-

    The three similar torque (t) are acting at an angle of 120º with each other. The resultant torque will be-

    PhysicsMechanics
    parallel
    Mechanics
    Physics

    A force of left parenthesis 2 i with hat on top minus 4 j with hat on top plus 2 k with hat on top right parenthesis  Newton acts at a point   left parenthesis 3 i with hat on top plus 2 j with hat on top minus 4 k with hat on top right parenthesis metre from the origin. The magnitude of torque is -

    A force of left parenthesis 2 i with hat on top minus 4 j with hat on top plus 2 k with hat on top right parenthesis  Newton acts at a point   left parenthesis 3 i with hat on top plus 2 j with hat on top minus 4 k with hat on top right parenthesis metre from the origin. The magnitude of torque is -

    PhysicsMechanics
    Mechanics
    Physics

    A disc is rotating with an angular velocity omega0. A constant retarding torque is applied on it to stop the disc. The angular velocity becomes (omega0/2) after n rotations. How many more rotations will it make before coming to rest?

    A disc is rotating with an angular velocity omega0. A constant retarding torque is applied on it to stop the disc. The angular velocity becomes (omega0/2) after n rotations. How many more rotations will it make before coming to rest?

    PhysicsMechanics
    Mechanics
    Physics

    A beam of length l lies on the +x axis with its left end on the origin. A cable pulls the beam in  y-direction with a force straight F equals straight F subscript 0 left parenthesis 1 minus straight x over ell right parenthesis.If the axis is fixed at x = 0 then find the torque

    A beam of length l lies on the +x axis with its left end on the origin. A cable pulls the beam in  y-direction with a force straight F equals straight F subscript 0 left parenthesis 1 minus straight x over ell right parenthesis.If the axis is fixed at x = 0 then find the torque

    PhysicsMechanics
    parallel

    card img

    With Turito Academy.

    card img

    With Turito Foundation.

    card img

    Get an Expert Advice From Turito.

    Turito Academy

    card img

    With Turito Academy.

    Test Prep

    card img

    With Turito Foundation.