Two bodies have moments of inertia $I_1 = I$ and $I_2 = 2I$ about their axes of rotation. If their rotational kinetic energies are equal,what is the ratio of their angular momenta?

During a test of a jet engine,its compressor rotates according to the graph shown. The total number of revolutions completed by the compressor during the test is:

$A$ uniform rod $AB$ of length $1 \ m$ and mass $4 \ kg$ is sliding along two mutually perpendicular frictionless walls $OX$ and $OY$. The velocity of the two ends of the rod $A$ and $B$ are $3 \ m/s$ and $4 \ m/s$ respectively, as shown in the figure. Which of the following statement$(s)$ is/are correct?

For the pivoted slender rod of length $l$ as shown in the figure,the angular velocity as the bar reaches the vertical position after being released from the horizontal position is:

$A$ thin ring of mass $2 \ kg$ has a radius of $0.5 \ m$. It is rolling without slipping on a horizontal plane with a velocity of $1 \ m/s$. $A$ small ball of mass $0.1 \ kg$ moving in the opposite direction with a velocity of $20 \ m/s$ hits the ring at a height of $0.75 \ m$ and moves vertically upward with a velocity of $10 \ m/s$ after the collision. Immediately after the collision:

$A$ ring of mass $m = 1 \ kg$ and radius $R = 1.25 \ m$ is kept on a rough horizontal ground. $A$ small body of same mass $m = 1 \ kg$ is stuck to the top of the ring. When it is given a slight push forward,the ring starts rolling purely on the ground. What is the maximum speed of the centre of the ring (in $m/s$)?