A thin wire of length L and uniform linear mass density is bent into a circular loop with centre at O as shown. The moment of inertia of the loop about the axis XX' is
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The one-quarter sector is cut from a uniform circular disc of radius R. This sector has mass M. It is made to rotate about a line perpendicular to its plane and passing through the centre of the original disc. Its moment of inertia about the axis of rotation is
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Let I be the moment of inertia of a uniform square plate about an axis AB that passes through its centre and is parallel to two of its sides. CD is a line in the plane of the plate that passes through the centre of the plate and makes an angle with AB. The moment of inertia of the plate about the axis CD is then equal to :
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A uniform rod of length 2L is placed with one end in contact with the horizontal and is then inclined at an angle to the horizontal and allowed to fall without slipping at contact point. When it becomes horizontal, its angular velocity will be
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A solid cylinder is rolling down on the inclined plane of angle . The coefficient of static friction between the plane and cylinder is The condition for the cylinder not to slip is
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A thin circular ring of mass M and radius r is rotating about its axis with a constant angular velocity . Two objects each of mass m are attached gently to the opposite ends of a diameter of the ring. The ring will now rotate with an angular velocity :
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A sphere rolls down on an inclined plane of inclination . What is the acceleration as the sphere reaches bottom ?
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A ball rolls without slipping. The radius of gyration of the ball about an axis passing through its centre of mass is K. If the radius of the ball is R, then the fraction of total energy associated with its rotational energy will be :
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A billiard ball of mass m and radius r, when hit in a horizontal direction by a cue at a height h above its centre, acquired a linear velocity . The angular velocity acquired by the ball is :
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Four thin rods of same mass M and same length l, form a square as shown in the figure. Moment of inertia of this system about an axis through centre O and perpendicular to its plane is :
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A mass m hangs with the help of a string wrapped around a pulley on a frictionless bearing. The pulley has mass m and radius R. Assuming pulley to be a perfect uniform circular disc, the acceleration of the mass m, if the string does not slip on the pulley, is
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A ladder is leaned against a smooth wall and it is allowed to slip on a frictionless floor. Which figure represents the trace of its center of mass?
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A carpet of mass m made of inextensible material is rolled along its length in the form of a cylinder of radius r and kept on a rough floor. The decrease in the potential energy of the system, when the carpet is unrolled to a radius without sliding is (g = acceleration due to gravity)
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From a solid sphere of mass M and radius R , a cube of maximum possible volume is cut. Moment of inertia of cube about an axis passing through its centre and perpendicular to one of its faces is :
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The moment of inertia of a uniform circular disc of radius 'R' and mass 'M' about an axis touching the disc at its edge and normal to the disc is :
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