From a circular ring of mass \({M}\) and radius \(R,\) an arc corresponding to a \(90^\circ\) sector is removed. The moment of inertia of the remaining part of the ring about an axis passing through the centre of the ring and perpendicular to the plane of the ring is \(K\) times \(MR^2.\) The value of \(K\) will be:
Question 2.
From a disc of radius \(R\) and mass \(M,\) a circular hole of diameter \(R,\) whose rim passes through the centre is cut. What is the moment of inertia of the remaining part of the disc about a perpendicular axis, passing through the centre?
Question 3.
A light rod of length \(l\) has two masses, \(m_1\) and \(m_2,\) attached to its two ends. The moment of inertia of the system about an axis perpendicular to the rod and passing through the centre of mass is:
Question 4.
Point masses \(m_1\) and \(m_2,\) are placed at the opposite ends of a rigid rod of length \(L\) and negligible mass. The rod is set into rotation about an axis perpendicular to it. The position of a point \(P\) on this rod through which the axis should pass so that the work required to set the rod rotating with angular velocity \(\omega_0\)is minimum is given by:
Question 5.
Three identical spherical shells, each of mass \(m\) and radius \(r\) are placed as shown in the figure. Consider an axis \(XX',\) which is touching two shells and passing through the diameter of the third shell. The moment of inertia of the system consisting of these three spherical shells about the \(XX'\) axis is:
Question 6.
The moment of inertia of a thin uniform rod of mass \(M\) and length \(L\) about an axis passing through its mid-point and perpendicular to its length is \(I_0\). Its moment of inertia about an axis passing through one of its ends and perpendicular to its length is:
Question 7.
A thin rod of length \(L\) and mass \(M\) is bent at its midpoint into two halves so that the angle between them is \(90^{\circ}\). The moment of inertia of the bent rod about an axis passing through the bending point and perpendicular to the plane defined by the two halves of the rod is:
Question 8.
The ratio of the radii of gyration of a circular disc to that of a circular ring, each of the same mass and radius, around their respective axes is:
Question 9.
The moment of inertia of a uniform circular disc of radius 'R' and mass 'M' about an axis passing from the edge of the disc and normal to the disc is:
Question 10.
The ratio of the radii of gyration of a circular disc about a tangential axis in the plane of the disc and of a circular ring of the same radius about a tangential axis in the
plane of the ring will be:
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Question 1.
A circular disc is to be made by using iron and aluminium
so that it acquires a maximum moment of inertia about its geometrical axis. It is possible with:
Question 2.
For the diagram given below, a triangular lamina is shown. The correct relation between I1, I2 & I3 is (I – moment of inertia)
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