$A$ dancer on a smooth floor is spinning about a vertical axis at an angular velocity of $20 \ rad/s$ with her arms folded. When she stretches her arms out,the angular speed decreases to $10 \ rad/s$. If the initial moment of inertia of the dancer is $I$,what will be the new moment of inertia?

$A$ dancer is standing on a rotating platform holding two spheres in her hands. If she drops the spheres to the ground,the dancer's...

Given below are two statements: One is labelled as Assertion $(A)$ and the other is labelled as Reason $(R)$.
Assertion $(A)$ : In a conical pendulum,angular momentum about its vertical axis remains constant.
Reason $(R)$ : Net torque about the vertical axis of a conical pendulum is not zero.
In the light of the above statements,choose the most appropriate answer from the options given below:

$A$ force $\vec F = \alpha \hat i + 3\hat j + 6\hat k$ is acting at a point $\vec r = 2\hat i - 6\hat j - 12\hat k$. The value of $\alpha$ for which angular momentum about the origin is conserved is:

When a body is spinning on its axis in the absence of any external torque,choose the wrong statement.

If the earth suddenly shrinks to $\frac{1}{64}$th of its original volume with its mass remaining the same,the period of rotation of earth becomes $\frac{24}{x} \text{ h}$. The value of $x$ is $.......$