A $T$ shaped object with dimensions shown in the figure, is lying a smooth floor. A force $\vec {'F'}$ is applied at the point $P$ parallel to $AB$, such that the object has only the translational motion without rotation. Find the location of $P$ with respect to $C$
$\frac {4}{3}l$
$l$
$\frac {2}{3}l$
$\frac {3}{2}l$
Radius of gyration of a uniform thin rod of length $L$ about an axis passing normally through its centre of mass is
In the $HCl$ molecule, the separation between the nuclei of the two atoms is about $1.27\,\mathop A\limits^o \left( {1\,\mathop A\limits^o = {{10}^{ - 10}}\,m} \right)$. The approximate location of the centre of mass of the molecule from hydrogen atom, assuming the chlorine atom to be about $35.5$ times massive as hydrogen is ....... $\mathop A\limits^o $
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
A ring of radius $4a$ is rigidly fixed in vertical position on a table. A small disc of mass $m$ and radius $a$ is released as shown in the fig. When the disc rolls down, without slipping, to the lowest point of the ring, then its speed will be
If the angular momentum of a body is increased by $200\,\%$ then increase in its rotational kinetic energy will be ....... $\%$.