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

$A$ man is pulling on a rope attached to a block on a smooth horizontal table. The tension in the rope will be the same at all points:

An inextensible string passing over a smooth pulley connects two blocks of masses $m_1$ and $m_2$ $(m_2 > m_1)$ vertically. If the acceleration of the system is $(\frac{g}{n})$, then the ratio of masses $(\frac{m_2}{m_1})$ is

Two identical blocks each of mass $M$ are attached to the ends of a massless inextensible string which passes over a pulley with a fixed axis as shown below. $A$ small mass $m$ is now placed on block $B$ (the right block). The acceleration with which the two blocks move together is ($g =$ gravitational acceleration).

Two masses of $1\, kg$ and $5\, kg$ are attached to the ends of a massless string passing over a pulley of negligible weight. The pulley itself is attached to a light spring balance as shown in the figure. When the masses are released and start moving,the reading of the spring balance will be:

The maximum acceleration with which a body of mass $200 \, kg$ is lowered into a well using a rope having a breaking force of $50 \, kg$-wt is (Acceleration due to gravity $= 10 \, ms^{-2}$) (in $ \, ms^{-2}$)