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 $C$
$\frac{4l}{3}$
$l$
$\frac{2l}{3}$
$\frac{3l}{2}$
Two objects of mass $10\,kg$ and $20\,kg$ respectively are connected to the two ends of a rigid rod of length $10\,m$ with negligible mass. The distance of the center of mass of the system from the $10\,kg$ mass is :
A firecracker is thrown with velocity of $30 \,ms ^{-1}$ in a direction which makes an angle of $75^{\circ}$ with the vertical axis. At some point on its trajectory, the firecracker splits into two identical pieces in such a way that one piece falls $27 \,m$ far from the shooting point. Assuming that all trajectories are contained in the same plane, how far will the other piece fall from the shooting point? (Take, $g=10 \,ms ^{-2}$ and neglect air resistance)
As shown in figure, when a spherical cavity (centred at $\mathrm{O})$ of radius $1$ is cut out of a uniform sphere of radius $\mathrm{R} \text { (centred at } \mathrm{C}),$ the centre of mass of remaining (shaded) part of sphere is at $G$, i.e, on the surface of the cavity. $\mathrm{R}$ can be detemined by the equation
Two masses $m_1$ and $m_2$ ($m_1$ > $m_2$) are connected by massless flexible and inextensible string passed over massless and frictionless pulley. The acceleration of center of mass is