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Seven identical disc are arranged in a hexagonal, planar pattern so as to touch each neighbour, as shown in the figure. Each disc has mass m and radius r. What is the moment of inertia of the system of seven disks about an axis passing through the centre of central disk and normal to plane of all disks?
Seven identical disc are arranged in a hexagonal, planar pattern so as to touch each neighbour, as shown in the figure. Each disc has mass m and radius r. What is the moment of inertia of the system of seven disks about an axis passing through the centre of central disk and normal to plane of all disks?
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A solid aluminium sphere of radius R has moment of inertia I about an axis through its centre. The moment of inertia about a central axis of a solid aluminium sphere of radius 2R is
A solid aluminium sphere of radius R has moment of inertia I about an axis through its centre. The moment of inertia about a central axis of a solid aluminium sphere of radius 2R is
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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 
(where 
is a positive constant). Then the moment of inertia of the ring about z-axis is :
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 (where is a positive constant). Then the moment of inertia of the ring about z-axis is :
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Two thin discs each of mass M and radius r are attached as shown in figure, to form a rigid body. The rotational inertia of this body about an axis perpendicular to the plane of disc B and passing through its centre is :
Two thin discs each of mass M and radius r are attached as shown in figure, to form a rigid body. The rotational inertia of this body about an axis perpendicular to the plane of disc B and passing through its centre is :
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Physics
Two spheres each of mass M and radius R/2 are connected at their centres with a mass less rod of length 2R. What will be the moment of inertia of the system about an axis passing through the centre of one of the sphere and perpendicular to the rod ?
Two spheres each of mass M and radius R/2 are connected at their centres with a mass less rod of length 2R. What will be the moment of inertia of the system about an axis passing through the centre of one of the sphere and perpendicular to the rod ?
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Figure show a thin metallic triangular sheet ABC. The mass of the sheet is M. The moment of inertia of the sheet about side AC is :
Figure show a thin metallic triangular sheet ABC. The mass of the sheet is M. The moment of inertia of the sheet about side AC is :
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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 :
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 :
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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 ?
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In a rectangle ABCD, AB =21 and BC=1. Axes 
and 
pass through centre of the rectangle . The moment of inertia is least about :
In a rectangle ABCD, AB =21 and BC=1. Axes and pass through centre of the rectangle . The moment of inertia is least about :
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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 :
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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
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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)
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Physics
Three point masses m1 ,m2 and 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 m1 ,m2 and 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 ?
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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
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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 
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 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
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