Three forces acting on a body are shown in the figure. To have the resultant force only along the $y-$ direction,the magnitude of the minimum additional force needed is ........... $N$.

$A$ bird weighs $2 \ kg$ and is inside a closed cage of $1 \ kg$. If it starts flying,then what is the weight of the bird and cage assembly in $kg$?

Given $m_1 = 4m_2$. The acceleration of $m_1$ is $a$. Find the velocity of $m_2$ at $t = 0.4 \, s$ in $cm/s$.

$A$ disc of mass $0.2 \ kg$ is kept floating in air without falling by vertically firing bullets each of mass $0.05 \ kg$ on the disc at the rate of $10$ bullets per second. If the bullets rebound with the same speed,then the speed of each bullet is (Acceleration due to gravity $g = 10 \ m \ s^{-2}$) (in $m \ s^{-1}$)

Statement $I :$ $A$ cyclist is moving on an unbanked road with a speed of $7 \, km/h$ and takes a sharp circular turn along a path of radius $2 \, m$ without reducing the speed. The static friction coefficient is $0.2$. The cyclist will not slip and pass the curve $(g = 9.8 \, m/s^2)$.
Statement $II :$ If the road is banked at an angle of $45^{\circ}$,the cyclist can cross the curve of $2 \, m$ radius with a speed of $18.5 \, km/h$ without slipping.

$A$ cold soft drink is kept on a balance. When the cap is opened,the weight reading on the balance: