Which of the following statements is true for a collision?

$A$ wooden block of mass $M$ is suspended by a cord and is at rest. $A$ bullet of mass $m$,moving with a velocity $v$,passes through the block and emerges with a velocity $v/2$ in the same direction. If the block rises to a height $H$,calculate the value of $H$.

$A$ pendulum of length $1 \,m$ and having a bob of mass $1 \,g$ is pulled aside through an angle $60^{\circ}$ with the vertical and then released. The power delivered by all the forces acting on the bob when the pendulum makes $30^{\circ}$ with the vertical is . . . . . . $\left(g=10 \,ms^{-2}\right)$ (in $\,mW$)

$A$ bob of mass $m$,suspended by a string of length $l_1$,is given a minimum velocity required to complete a full circle in the vertical plane. At the highest point,it collides elastically with another bob of mass $m$ suspended by a string of length $l_2$,which is initially at rest. Both the strings are massless and inextensible. If the second bob,after collision,acquires the minimum speed required to complete a full circle in the vertical plane,the ratio $\frac{l_1}{l_2}$ is

$A$ particle of mass $m$ is dropped from a height $h$ above the ground. At the same time,another particle of the same mass is thrown vertically upwards from the ground with a speed of $\sqrt{2gh}$. If they collide head-on completely inelastically,the time taken for the combined mass to reach the ground,in units of $\sqrt{\frac{h}{g}}$,is

$A$ body of mass $2 \,kg$ is moving with a constant acceleration of $(2 \hat{i}+3 \hat{j}-\hat{k}) \,ms^{-2}$. If the displacement made by the body is $(3 \hat{i}-\hat{j}+2 \hat{k}) \,m$, then the work done is: (in $\,J$)