A rod $P$ of length $1\ m$ is hinged at one end $A$ and there is a ring attached to the other end by a light inextensible thread . Another long rod $Q$ is hinged at $B$ and it passes through the ring. The rod $P$ is rotated about an axis which is perpendicular to plane in which both the rods are present and the variation between the angles $\theta $ and $\phi $ are plotted as shown. The distance between the hinges $A$ and $B$ is ........ $m.$
$3$
$2$
$1$
$0.5$
Two bodies of mass $1\,kg$ and $3\,kg$ have position vectors $\hat i\,\, + \,\,2\hat j\,\, + \,\,\hat k$ and $-\,3\hat i\,\, - \,\,2\hat j\,\, + \,\,\hat k$, respectively. The centre of mass of this system has a position vector
A uniform metre stick of mass $M$ is hinged at one end and supported in a horizontal direction by a string attached to the other end. What should be the initial angular acceleration of free end of the stick if the string is cut? (in $rad/sec^2$ )
We have two spheres one of which is hollow and the other solid. They have identical masses and moment of inertia about their respectively diameters. The ratio of their radius is given by
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
A thin rod of length $L$ and mass $M$ is bent at its mid-point into two halves so that the angle between them is $90^o$. 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