A small object of uniform density rolls up a curved surface with an initial velocity $$v$$. It reaches up to a maximum height of $$\frac{3 v^{2}}{4 g}$$ with respect to the initial position. The object is

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.

Two discs $A$ and $B$ are mounted coaxially on a vertical axle. The discs have moment of inertia $I$ and $2 I$ respectively about the common axis. Disc $A$ is imparted an initial angular velocity $2 \omega$ using the entire potential energy of a spring compressed by a distance $x_1$. Disc $B$ is imparted an angular velocity $\omega$ by a spring having the same spring constant and compressed by a distance $x_2$. Both the discs rotate in the clockwise direction.

The ratio $${{{x_1}} \over {{x_2}}}$$ is

Two discs $A$ and $B$ are mounted coaxially on a vertical axle. The discs have moment of inertia $I$ and $2 I$ respectively about the common axis. Disc $A$ is imparted an initial angular velocity $2 \omega$ using the entire potential energy of a spring compressed by a distance $x_1$. Disc $B$ is imparted an angular velocity $\omega$ by a spring having the same spring constant and compressed by a distance $x_2$. Both the discs rotate in the clockwise direction.

When disc B is brought in contact with disc A, they acquire a common angular velocity in time t. The average frictional torque on one disc by the other during this period is