$A$ slender uniform rod of length $\lambda$ is balanced vertically at a point $P$ on a horizontal surface having some friction. If the top of the rod is displaced slightly to the right, the position of its centre of mass at the time when the rod becomes horizontal :
lies at some point to the right of $P$
lies at some point to the left of $P$
must be $\lambda /2$ to the right of $P$
lies at $P$
Two uniform plates of the same thickness and area but of different materials, one shaped like an isosceles triangle and the other shaped like a rectangle are joined together to form a composite body as shown in the figure alongside.If the centre of mass of the composite body is located at the mid-point of their common side, then the ratio between masses of the triangle to that of the rectangle is
The linear mass density $(\lambda)$ of a rod of length $L$ kept along $x$-axis varies as $\lambda=\alpha+\beta x$; where $\alpha$ and $\beta$ are positive constants. The centre of mass of the rod is at ..........
Two masses $M$ and $m$ are attached to a vertical axis by weightless threads of combined length $l$. They are set in rotational motion in a horizontal plane about this axis with constant angular velocity $\omega $. If the tensions in the threads are the same during motion, the distance of $M$ from the axis is
From a uniform disc of radius $R$, an equilateral triangle of side $\sqrt 3 \,R$ is cut as shown. The new position of centre of mass is :
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 $C$