$A$ balloon carrying some sand of mass $M$ is moving down with a constant acceleration $a_0$. The mass $m$ of sand to be removed so that the balloon moves up with double the acceleration $2a_0$ is:

The mass of a lift is $2000 \, kg$. When the tension in the supporting cable is $28000 \, N$,then its acceleration is:

$A$ block of mass $M$ is placed on a horizontal surface and 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 the surface between $M$ and $m_0$ has a coefficient of friction $\mu$,find the tension in the string,assuming the system moves together.

What will be the acceleration of the system and tension in the rope connecting $5\,kg$ and $1\,kg$ blocks?

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

$A$ block of mass $4 \,kg$ is suspended through two light spring balances $A$ and $B$ as shown in the figure. Then $A$ and $B$ will read respectively: