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Mechanics

Physics

$straight A space smooth space tube space of space certain space mass space is space rotated space in space straight a space gravity minus free space space space and space released. space The space two space balls space shown space in space Fig. space move space towards space the space ends space of space the space tube. space For space the space whole space system comma space which space of space the space following space quantities space is space not space conserved.$

$straight A space smooth space tube space of space certain space mass space is space rotated space in space straight a space gravity minus free space space space and space released. space The space two space balls space shown space in space Fig. space move space towards space the space ends space of space the space tube. space For space the space whole space system comma space which space of space the space following space quantities space is space not space conserved.$

PhysicsMechanics

Mechanics

Physics

$straight A space thin space uniform space rod space of space mass space straight m space and space length space l space is space kept space on space straight a space smooth space horizontal space surface space such space that space it space can space move space freely. space At space what space distance space from space centre space of space rod space should space straight a space particle space of space mass space straight m space strike space on the space rod space such space that space the space point space straight P space at space straight a space distance italic space l italic divided by italic 3 space from space the space end space of space the space rod space is space instantaneously space at space rest space just space after space the space elastic space collision ? space$

$straight A space thin space uniform space rod space of space mass space straight m space and space length space l space is space kept space on space straight a space smooth space horizontal space surface space such space that space it space can space move space freely. space At space what space distance space from space centre space of space rod space should space straight a space particle space of space mass space straight m space strike space on the space rod space such space that space the space point space straight P space at space straight a space distance italic space l italic divided by italic 3 space from space the space end space of space the space rod space is space instantaneously space at space rest space just space after space the space elastic space collision ? space$

PhysicsMechanics

Mechanics

Physics

$straight A space cube space of space side space straight a space and space mass space straight m space is space to space be space tilted space at space point space straight A space by space applying space straight a space force space straight F space as space shown space in space Fig. space The space minimum space force space required space is$

$straight A space cube space of space side space straight a space and space mass space straight m space is space to space be space tilted space at space point space straight A space by space applying space straight a space force space straight F space as space shown space in space Fig. space The space minimum space force space required space is$

PhysicsMechanics

Mechanics

Physics

$Three space point space masses space straight m subscript 1 space comma straight m subscript 2 space and space space straight m subscript 3 space are space located space at space the space vertices space of space an space equilateral space triangle space of space side space apostrophe space straight a apostrophe space. space What space is space the space moment space of space inertia space of space the space system space about space an space axis space along space the space altitude space of space the space triangle space passing space through space straight m subscript 1 space space ?$

$Three space point space masses space straight m subscript 1 space comma straight m subscript 2 space and space space straight m subscript 3 space are space located space at space the space vertices space of space an space equilateral space triangle space of space side space apostrophe space straight a apostrophe space. space What space is space the space moment space of space inertia space of space the space system space about space an space axis space along space the space altitude space of space the space triangle space passing space through space straight m subscript 1 space space ?$

PhysicsMechanics

Mechanics

Physics

$straight A space uniformthin space rod space of space length italic space l italic space and space mass space straight m space is space hinged space at space straight a space distance italic space l italic divided by italic 4 space space from space one space of space the space end space and space released space from space horizontal space position space as space shown space in space Fig. The space angular space velocity space of space the space rod space as space it space passes the space vertical space position space is$

$straight A space uniformthin space rod space of space length italic space l italic space and space mass space straight m space is space hinged space at space straight a space distance italic space l italic divided by italic 4 space space from space one space of space the space end space and space released space from space horizontal space position space as space shown space in space Fig. The space angular space velocity space of space the space rod space as space it space passes the space vertical space position space is$

PhysicsMechanics

Mechanics

Physics

$In space figure comma space the space bar space is space uniform space and space weighting space 500 straight N. space How space large space must space straight W space be space if space T subscript 1 space space and space T subscript 2 space space are space to space be space equal space ?$

$In space figure comma space the space bar space is space uniform space and space weighting space 500 straight N. space How space large space must space straight W space be space if space T subscript 1 space space and space T subscript 2 space space are space to space be space equal space ?$

PhysicsMechanics

Mechanics

Physics

$straight A space string space is space wrapped space around space straight a space cylinder space of space mass space straight M space and space radius space straight R. space The space string space is space pulled space vertically space upwards space to space prevent space the space canto space of space mass space from space falling space as space the space cylinder space unwinds space the space string. space The space tension space in space the space string space is space$

$straight A space string space is space wrapped space around space straight a space cylinder space of space mass space straight M space and space radius space straight R. space The space string space is space pulled space vertically space upwards space to space prevent space the space canto space of space mass space from space falling space as space the space cylinder space unwinds space the space string. space The space tension space in space the space string space is space$

PhysicsMechanics

Mechanics

Physics

$straight A space uniform space disc space of space mass space straight M space and space radius space straight R space is space mounted space on space an space axle space supported space in space frictionless space bearings. space straight A space light space cord space is space wrapped space around space the space rim space of space the space disc space and space straight a space steady space downward space pull space straight T space is space exerted space on space the space cord. space The space angular space acceleration space of space the space disc space is$

$straight A space uniform space disc space of space mass space straight M space and space radius space straight R space is space mounted space on space an space axle space supported space in space frictionless space bearings. space straight A space light space cord space is space wrapped space around space the space rim space of space the space disc space and space straight a space steady space downward space pull space straight T space is space exerted space on space the space cord. space The space angular space acceleration space of space the space disc space is$

PhysicsMechanics

Mechanics

Physics

$Two space rings space of space same space radius space and space mass space are space placed space such space that space their space centres space are space at space straight a space space common space point space and space their space planes space are space perpendicular space to space each space other. space The space moment space of space inertia space of space the space system space about space an space axis space passing space through space the space centre space and space perpendicular space to space the space plane space of space one space of space the space rings space is space left parenthesis mass space of space the space ring space equals space straight m comma space radius space equals space straight r right parenthesis$

$Two space rings space of space same space radius space and space mass space are space placed space such space that space their space centres space are space at space straight a space space common space point space and space their space planes space are space perpendicular space to space each space other. space The space moment space of space inertia space of space the space system space about space an space axis space passing space through space the space centre space and space perpendicular space to space the space plane space of space one space of space the space rings space is space left parenthesis mass space of space the space ring space equals space straight m comma space radius space equals space straight r right parenthesis$

PhysicsMechanics

Mechanics

Physics

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?

PhysicsMechanics

Mechanics

Physics

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

PhysicsMechanics

Mechanics

Physics

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 $lambda equals lambda subscript 0 cos squared theta$ (where $lambda subscript 0$ 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 $lambda equals lambda subscript 0 cos squared theta$ (where $lambda subscript 0$ is a positive constant). Then the moment of inertia of the ring about z-axis is :

PhysicsMechanics

Mechanics

Physics

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 :

PhysicsMechanics

Mechanics

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 ?

PhysicsMechanics

Mechanics

Physics

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 I_A and I_B 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 I_A and I_B about the same axis is :

PhysicsMechanics

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