$A$ system containing masses and pulleys connected on an inclined plane is shown in the figure. If the system is in equilibrium, then the value of $m$ is (in $\,kg$)

If the breaking strength of a rope is $\frac{4}{3}$ times the weight of a person,then the maximum acceleration with which the person can safely climb up the rope is ($g$ = acceleration due to gravity).

The figure shows two blocks connected by a light inextensible string. $A$ force of $10 \,N$ is applied on the bigger block at $60^{\circ}$ with the horizontal. The tension in the string connecting the two masses is ....... $N$.

$A$ block of mass $M$ is placed on a horizontal surface and it is tied with an inextensible string to a block of mass $m$,as shown in the figure. $A$ block of mass $m_0$ is also placed on $M$. If $\mu < \mu_{min}$ (the minimum friction required to keep the block $m$ stationary),then the downward acceleration of $m$ is:

$A$ constant horizontal force $\overrightarrow{F}$ of magnitude $10 \,N$ is applied to a block $A$ and this produces an acceleration of magnitude $20 \,m/s^2$. If this block $A$ is then kept against another block $B$ of mass $1.5 \,kg$ as shown in the figure and a force $F^{\prime}$ of $20 \,N$ is applied, find the force on the block $B$. Neglect friction. (in $N$)

$A$ force $F = 10t$ acts on a block of mass $m = 10 \, kg$ as shown in the figure. The coefficient of friction is $\mu = 0.4$. Find the time $t$ when the block loses contact with the surface.