In the figure shown find out the distance of centre of mass of a system of a uniform circular plate of radius $3R$ from $O$ in which a hole of radius $R$ is cut whose centre is at $2R$ distance from centre of large circular plate
$R/4$
$R/5$
$R/2$
None of these
A semicircular portion of radius $'r'$ is cut from a uniform rectangualr plate as shown in figure. The distance of centre of mass $'C'$ of remaining plate, from point $'O'$ is
$A$ 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 :
A circular plate of uniform thickness of diameter $56\, cm$, whose center is at origin. A circular part of diameter $42\, cm$ is removed from one edge. What is the distance of the centre of mass of the remaining part ........ $cm.$
A spherical hollow is made in a lead sphere of radius $R,$ such that its surface touches the outside surface of lead sphere and passes through the centre. What is the shift in the centre of mass of lead sphere due to the following ?
A wheel in uniform motion about an axis passing through its centre and perpendicular to its plane is considered to be in mechanical (translational plus rotational) equilibrium because no net external force or torque is required to sustain its motion. However, the particles that constitute the wheel do experience a centripetal the acceleration directed towards the centre. How do you reconcile this fact with the wheel being in equilibrium?
How would you set a half wheel into uniform motion about an axis passing through the centre of mass of the wheel and perpendicular to its plane? Will you require external forces to sustain the motion ?