$A$ block of mass $1\,kg$ is suspended by a string of mass $1\,kg$ and length $1\,m$ as shown in the figure. Given $g = 10\,m/s^2$,calculate the tension in the string at its mid-point. (in $,N$)

The breaking stress of a wire going over a smooth pulley is $2 \times 10^9\, N/m^2$. What would be the minimum radius of the wire used if it is not to break? (Assume $g = 10\, m/s^2$)

$A$ frictionless pulley is attached to one arm of a balance and a string passed around it carries two masses $m_1$ and $m_2$. The pulley is provided with a clamp due to which $m_1$ and $m_2$ do not move with respect to each other. On removing the clamp,$m_1$ and $m_2$ start moving. How much change in counter mass has to be made to restore balance?

In the arrangement shown,the mass $m$ will ascend with an acceleration (Pulley and rope are massless).

The acceleration of the $2\,kg$ block if the free end of the string is pulled with a force of $20\,N$ as shown in the figure is:

For the pulley system shown in the figure,calculate the kinetic energy of the $6\,kg$ block after $5\,s$. (Assume $g = 10\,m/s^2$)