On a stationary sail-boat,air is blown at the sails from a fan attached to the boat. The boat will

$A$ balloon of mass $M$ is descending at a constant acceleration $\alpha$. When a mass $m$ is released from the balloon,it starts rising with the same acceleration $\alpha$. Assuming that its volume does not change,what is the value of $m$?

In which of the following graphs,the total change in momentum is zero?

$A$ ball of mass $0.1\, kg$ is whirled in a horizontal circle of radius $1\, m$ by means of a string at an initial speed of $10\, rpm$. Keeping the radius constant,the tension in the string is reduced to one-quarter of its initial value. The new speed is ....... $rpm$.

$A$ $300\ kg$ crate is dropped vertically onto a conveyor belt that is moving at $1.20\ m/s$. $A$ motor maintains the belt's constant speed. The belt initially slides under the crate,with a coefficient of friction of $0.400$. After a short time,the crate is moving at the speed of the belt. During the period in which the crate is being accelerated,find the work done by the motor which drives the belt :- ................. $J$

An object of mass $10 \,kg$ is projected from the ground with a speed of $40 \,m/s$ at an angle of $60^{\circ}$ with the horizontal. The rate of change of momentum of the object one second after projection in $SI$ units is ........ [Take $g = 9.8 \,m/s^2$]