$A$ bullet of mass $m_1$ is moving with speed $v_0$ and hits a sand bag of mass $m_2$. If the speed of the bullet after passing through the sand bag is $\frac{v_0}{3}$,then the height $h$ up to which the bag rises is (assume,$g=$ acceleration due to gravity).

The velocity of the bullet becomes one-third after it penetrates $4 \ cm$ in a wooden block. Assuming that the bullet faces a constant resistance during its motion in the block,the bullet stops completely after traveling a total distance of $(4+x) \ cm$ inside the block. The value of $x$ is $.....$ (in $cm$)

Two identical $5\,kg$ blocks are moving with the same speed of $2\,m/s$ towards each other along a frictionless horizontal surface. The two blocks collide,stick together,and come to rest. Considering the two blocks as a system,the work done on the system by the external forces will be ............. $Joule$.

$A$ and $B$ are blocks of same mass $m$ exactly equivalent to each other. Both are placed on a frictionless surface connected by a spring. The natural length of the spring is $L$ and the force constant is $K$. Initially,the spring is at its natural length. Another equivalent block $C$ of mass $m$ travelling at speed $v$ along the line joining $A$ and $B$ collides with $A$. In an ideal condition,the maximum compression of the spring is:

$A$ target is made of two plates,one of wood and the other of iron. The thickness of the wooden plate is $4\,cm$ and that of the iron plate is $2\,cm$. $A$ bullet fired goes through the wood first and then penetrates $1\,cm$ into the iron. $A$ similar bullet fired with the same velocity from the opposite direction goes through the iron first and then penetrates $2\,cm$ into the wood. If $a_1$ and $a_2$ are the retardations offered to the bullet by the wood and iron plates respectively,then:

$A$ circular well of diameter $2 \ m$ has water up to the ground level. If the bottom of the well is at a depth of $14 \ m$,the time taken in seconds to empty the well using a $1.4 \ kW$ motor is (Acceleration due to gravity $= 10 \ m \ s^{-2}$)