Five masses each of $2\, kg$ are placed on a horizontal circular disc, which can be rotated about a vertical axis passing through its centre and all the masses be equidistant from the axis and at a distance of $10\, cm$ from it. The moment of inertia of the whole system (in $gm-cm^2$ ) is: (Assume disc is of negligible mass)
$10^5$
$10^4$
$10^6$
$10^8$
Two rotating bodies $A$ and $B$ of masses $m$ and $2\,m$ with moments of innertia $I_A$ and $I_B\,(I_B > I_A)$ have equal kinetic energy of rotation. If $L_A$ and $L_B$ be their angular momentum respectively, then
A thin wire of length $\ell$ and mass $m$ is bent in the form of a semicircle as shown. Its moment of inertia about an axis joining its free ends will be ...........
A disc of mass $M$ and radius $R$ rolls on a horizontal surface and then rolls up an inclined plane as shown in the figure. If the velocity of the disc is $v,$ the height to which the disc will rise will be
A uniform cube of side $a$ and mass $m$ rests on a rough horizontal table. A horizontal force $F$ is applied normal to one of the faces at a point that is directly above the centre of face, at a height $\frac {3a}{4}$ above the base. The minimum value of $F$ for which the cube begins to tilt about the edge is (Assume that the cube does not slide)
A thin circular ring of mass $M$ and radius $r$ is rotating about its axis with a constant angular velocity $\omega $ . Two objects each of mass $m$ are attached gently to the opposite ends of a diameter of the ring. The ring will now rotate with an angular velocity