Two blocks of mass $M_1 = 20\,kg$ and $M_2 = 12\,kg$ are connected by a metal rod of mass $8\,kg$. The system is pulled vertically up by applying a force of $480\,N$ as shown. The tension at the mid-point of the rod is ........ $N$.

Two particles each of mass $m$ are moving in horizontal circles with the same angular speed $\omega$. If both strings are of the same length $l$,find the ratio of tension in the strings $\frac{T_1}{T_2}$.

Two masses $M$ and $m$ are connected by a weightless string. They are pulled by a force $F$ on a frictionless horizontal surface as shown in the figure. The tension in the string will be

With what acceleration can a block be moved upwards using a rope,if the breaking strength of the rope is $5$ times the weight of the block?

$A$ body of mass $8\,kg$ is hanging from another body of mass $12\,kg$. The combination is being pulled upwards by a string with an acceleration of $2.2\,m/s^2$. The tensions $T_1$ (in the top string) and $T_2$ (in the string between the two masses) will be respectively: (use $g = 9.8\,m/s^2$)

$A$ monkey of mass $40 \, kg$ climbs on a rope which can stand a maximum tension of $600 \, N$. In which of the following cases will the rope break: the monkey
$(a)$ climbs up with an acceleration of $6 \, m \, s^{-2}$
$(b)$ climbs down with an acceleration of $4 \, m \, s^{-2}$
$(c)$ climbs up with a uniform speed of $5 \, m \, s^{-1}$
$(d)$ falls down the rope nearly freely under gravity? (Ignore the mass of the rope).