$A$ thin string is wrapped around the circumference of a wheel of radius $r$. The wheel has a horizontal axle and a moment of inertia $I$ about it. $A$ weight $mg$ is attached to the end of the string,which falls from rest. After falling through a distance $h$,the angular velocity of the wheel will be:

$STATEMENT-1$ If there is no external torque on a body about its center of mass,then the velocity of the center of mass remains constant. because
$STATEMENT-2$ The linear momentum of an isolated system remains constant.

State the equivalent physical quantities in linear motion corresponding to the moment of inertia and torque in rotational motion.

$A$ thin uniform bar of length $L$ and mass $8m$ lies on a smooth horizontal table. Two point masses $m$ and $2m$ move in the same horizontal plane from opposite sides of the bar with speeds $2v$ and $v$ respectively. The masses stick to the bar after collision at distances $L/3$ and $L/6$ respectively from the center of the bar. If the bar starts rotating about its center of mass as a result of the collision,the angular speed of the bar will be

$A$ projectile of mass $3m$ explodes at the highest point of its path. It breaks into three equal parts. One part retraces its path,the second one comes to rest. The distance of the third part from the point of projection when it finally lands on the ground is ........$m.$ (The range of the projectile was $100\,m$ if no explosion would have taken place.)

$Assertion$ : $A$ helicopter must necessarily have two propellers.
$Reason$ : Two propellers are provided in a helicopter in order to conserve linear momentum.