For the given figure,the tension in the string $T_1$ is .......... $N$.

$A$ 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:

An elevator accelerates upwards at a constant rate. $A$ uniform string of length $L$ and mass $m$ supports a small block of mass $M$ that hangs from the ceiling of the elevator. The tension at distance $l$ from the ceiling is $T$. The acceleration of the elevator is

An elevator of mass $m$ is connected to a rope which pulls the elevator up with a maximum acceleration equal to $a$. If the maximum bearable tension in the rope is $T$,then for a safe journey the minimum diameter of the rope is $[g=$ acceleration due to gravity$]$

On a smooth plane surface,two blocks $A$ and $B$ are accelerated by applying a force of $15 \, N$ on block $A$. If the mass of block $B$ is twice that of block $A$,the force on block $B$ is ........... $N$.

$A$ block of mass $m_1$ rests on a horizontal table. $A$ string tied to the block is passed over a frictionless pulley fixed at the end of the table,and to the other end of the string is hung another block of mass $m_2$. The acceleration of the system is