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Physics

Mechanics

Easy

Question

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

$2 \sqrt{\frac{5 g}{7 l}}$
$2 \sqrt{\frac{6 g}{7 l}}$
$\sqrt{\frac{3 g}{7 l}}$
$2 \sqrt{\frac{g}{l}}$

The correct answer is: $2 square root of fraction numerator 6 g over denominator 7 l end fraction end root$

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PhysicsMechanics

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PhysicsMechanics

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

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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 :

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PhysicsMechanics

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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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 :

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PhysicsMechanics

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PhysicsMechanics

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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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PhysicsMechanics

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

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PhysicsMechanics

Three point masses m₁,m₂and 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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