What is the minimum acceleration with which a person can slide down a rope,if the breaking strength of the rope is $\frac{2}{3}$ of the person's weight?

$A$ small ball $B$ of mass $m$ is suspended with a light inelastic string of length $L$ from a block $A$ of the same mass $m$,which can move on a smooth horizontal surface as shown in the figure. The ball is displaced by an angle $\theta$ from the equilibrium position and then released. The maximum velocity of the block during the subsequent motion of the system after the release of the ball is

$A$ block of mass $m$ is connected to another block of mass $M$ by a massless spring of spring constant $k$. The blocks are kept on a smooth horizontal plane. Initially,the blocks are at rest and the spring is unstretched. Then a constant force $F$ starts acting on the block of mass $M$ to pull it. Find the force acting on the block of mass $m$.

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 ....... $N$.

An $80\, kg$ person is parachuting and is experiencing a downward acceleration of $2.8\, m/s^2$. The mass of the parachute is $5\, kg$. The upward force on the open parachute is ........... $N$ (Take $g = 9.8\, m/s^2$)

$A$ lift of mass $m$ is ascending with an acceleration $a$ $(a < g)$. The tension in the cable of the lift is $(g = \text{acceleration due to gravity})$