From a circle of radius $a,$ an isosceles right angled triangle with the hypotenuse as the diameter of the circle is removed. The distance of the centre of gravity of the remaining position from the centre of the circle is
$3(\pi - 1)a$
$\frac{{(\pi - 1)a}}{6}$
$\frac{a}{{3\,(\pi - 1)}}$
$\frac{a}{{3\,(\pi + 1)}}$
A stick has its bottom end attached to a wall by a pivot and is held up by a massless string attached to its other end. Which of the following scenarios has the smallest tension in the string ? (Length of stick is same in all scenarios)
A circular plate of diameter ' $a$ ' is kept in contact with a square plate of side $a$ as shown. The density of the material and the thickness are same everywhere. The centre of mass of composite system will be ...........
A circular hole of radius $\left(\frac{ a }{2}\right)$ is cut out of a circular disc of radius $'a'$ as shown in figure. The centroid of the remaining circular portion with respect to point $'O'$ will be :
A rod of length is $3 \;m$ and its mass acting per unit length is directly proportional to distance $x$ from one of its end then its centre of gravity from that end will be at
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 :