A particle originally at rest at the highest point of $a$ smooth vertical circle is slightly displaced. It will leave the circle at $a$ vertical distance $h$ below the highest point, such that
$h = R$
$h = R/3$
$h = R/2$
$h = 2R$
A disc is rotating with an angular velocity $\omega_0$. A constant retarding torque is applied on it to stop the disc. The angular velocity becomes $\frac{{{\omega _0}}}{2}$ after $n$ rotations. How many more rotations will it make before coming to rest
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 $C$
Four particles of masses $1\,kg, 2 \,kg, 3 \,kg$ and $4\, kg$ are placed at the four vertices $A, B, C$ and $D$ of a square of side $1\, m$. The coordinates of centre of mass of the particles are
Find the torque of a force $\vec F = -3\hat i + \hat j + 5\hat k$ acting at the point $\vec r = 7\hat i + 3\hat j + \hat k$ with respect to origin
The linear mass density of a rod of length $L$ varies as $\lambda = kx^2$, where $k$ is a constant and $x$ is the distance from one end. The position of centre of mass of the rod is