In the case of a wire having negligible mass,suspended from a ceiling and stretched under the action of a weight $F$ suspended from its other end,the tension at any cross-section of the wire is

$A$ mass of $1 \ kg$ is suspended by a string $A$. Another string $C$ is connected to its lower end (see figure). If the string $C$ is stretched slowly,then

One end of a string of length $l$ is connected to a particle of mass $m$ and the other to a small peg on a smooth horizontal table. If the particle moves in a circle with speed $v$,the net force on the particle (directed towards the centre) is ($T$ is the tension in the string).

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 $g = 10\, m/s^2$)

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

$A$ student calculates the acceleration of $m_1$ in the figure shown as $a_1 = \frac{(m_1 - m_2)g}{m_1 + m_2}$. Which assumption is not required to do this calculation?