$A$ balloon with mass $m$ is descending down with an acceleration $a$ (where $a < g$). How much mass should be removed from it so that it starts moving up with an acceleration $a$?

Which of the following statements is not true?

Two situations are shown in figures $(a)$ and $(b)$. In each case,$m_1 = 3 \ kg$ and $m_2 = 4 \ kg$. If $a_1$ and $a_2$ are the respective accelerations of the blocks in these situations,then the values of $a_1$ and $a_2$ are respectively [ $g = 10 \ ms^{-2}$ ]

$A$ ball rests upon a flat piece of paper on a table top. The paper is pulled horizontally but quickly towards the right as shown. Relative to its initial position with respect to the table,the ball:
$(A)$ Remains stationary if there is no friction between the paper and the ball.
$(B)$ Moves to the left and starts rolling backwards,$i.e.$,to the left if there is friction between the paper and the ball.
$(C)$ Moves forward,$i.e.$,in the direction in which the paper is pulled.
Which of the following statements is/are correct?

Fill in the blanks:
$(a)$ $A$ load of $3 \, kg$ is suspended from a rope of $6 \, kg$. The tension at the top end of the rope is ...........
$(b)$ The effect produced by a force $F$ acting for a time $\Delta t$ is the same as that produced by a force $2F$ acting for a time ...........
$(c)$ Friction ........... due to excessive ironing.

$A$ $100 \, kg$ gun fires a ball of $1 \, kg$ horizontally from a cliff of height $500 \, m$. It falls on the ground at a distance of $400 \, m$ from the bottom of the cliff. Find the recoil velocity of the gun. (Acceleration due to gravity $g = 10 \, m/s^2$) (in $, m/s$)