MHT-CET (DEMO) PHYSICS SYSTEM OF PARTICLES AND ROTATIONAL MOTION PAPER

From a circular ring of mass $$M$$ and $$R$$, 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 ring and perpendicular to the plane of ring is $$k$$ times $$M R^{2}$$. Then the value of $$k$$ is

A solid sphere of radius $$R$$ has moment of inertia $$I$$ about its geometrical axis. If it is melted into a disc of radius $$r$$ and thickness $$t$$. If its moment of inertia about the tangential axis (which is perpendicular to plane of the disc), is also equal to $$I$$, then the value of $$r$$ is equal to

Moment of inertia of a disc about an axis which is tangent and parallel to its plane is $$I$$. Then the moment of inertia of disc about a tangent, but perpendicular to its plane will be

Moment of inertia of big drop in I. If 8 droplets are formed from big drop, then moment of inertia of small droplet is

A spherical shell has mass $$M$$ and radius $$R$$. Moment of inertia about its diameter will be

The moment of inertia of a body does not depend upon

From a circular disc of radius $$R$$ and mass $$9 M$$, a small disc of radius $$R / 3$$ is removed from the disc. The moment of inertia of the remaining disc about an axis perpendicular to the plane of the disc and passing through $$O$$ is

From a circular disc of radius $$R$$ and mass $$9 M$$, a small disc of mass $$M$$ and radius $$\frac{R}{3}$$ is removed concentrically. The moment of inertia of the remaining disc about an axis perpendicular to the plane of the disc and passing through its center is

A wheel of mass 10 kg has a moment of inertia of $$160 \mathrm{~kg}-\mathrm{m}^{2}$$ about its own axis, the radius of gyration will be

Moment of inertia of a thin circular disc of mass $$M$$ and radius $$R$$ about any diameter is

Two solid cylinders $$P$$ and $$Q$$ of same mass and same radius start rolling down a fixed inclined plane from the same height at the same time. Cylinder $$P$$ has most of its mass concentrated near its surface, while $$Q$$ has most of its mass concentrated near the axis. Which statement (s) is (are) correct

A rod of length $$l$$ is hinged at one end and kept horizontal. It is allowed to fall. The velocity of the other end of the rod is

Point masses $$1,2,3$$ and 4 kg are lying at the point $$(0,0,0),(2,0,0),(0,3,0)$$ and $$(-2,-2,0)$$ respectively. The moment of inertia of this system about $$x$$-axis will be

Moment of inertia of ring about its diameter is $$I$$. Then, moment of inertia about an axis passing through center perpendicular to its plane is

The moment of inertia of a rod about an axis through its center and perpendicular to it is $$\frac{1}{2} M L^{2}$$ (where $$M$$ is the mass and $$L$$ is the length of the rod). The rod is bent in the middle so that the two halves makes an angular of $$60^{\circ}$$. The same axis would be