Two blocks of mass $1\ kg$ and $2\ kg$ are connected with each other by a spring of spring constant $60\ N/m$. If the velocity given to the block of mass $2\ kg$ at the natural length is $6\ m/s$,find the maximum velocity of the $1\ kg$ block in the subsequent motion (in $m/s$).

The left end of a massless stick with length $l$ is placed on the corner of a table,as shown in the figure. $A$ point mass $m$ is attached to the center of the stick,which is initially held horizontal. It is then released. Immediately afterward,what normal force does the table exert on the stick?

$A$ uniform rod is rotating in a gravity-free region with a certain constant angular velocity $\omega$. The variation of tensile stress $\sigma$ with distance $x$ from the axis of rotation is best represented by which of the following graphs?

What is pure translational motion?

In the following figure,a body of mass $m$ is tied at one end of a light string and this string is wrapped around a solid cylinder of mass $M$ and radius $R$. At the moment $t = 0$,the system starts moving. If the friction is negligible,the angular velocity at time $t$ would be

Point masses $m_1$ and $m_2$ are placed at the opposite ends of a rigid rod of length $L$ and negligible mass. The rod is to be set rotating about an axis perpendicular to it. The position of point $P$ on this rod through which the axis should pass so that the work required to set the rod rotating with angular velocity $\omega_0$ is minimum,is given by