Statement 1 :

A block of mass m starts moving on a rough horizontal surface with a velocity v. It stops due to friction between the block and the surface after moving through a certain distance. The surface is now tilted to an angle of 30$$^\circ$$ with the horizontal and the same block is made to go up on the surface with the same initial velocity v. The decrease in the mechanical energy in the second situation is smaller than that in the first situation.

Statement 2 :

The coefficient of friction between the block and the surface decreases with the increase in the angle of inclination.

Statement 1 :

In an elastic collision between two bodies, the relative speed of the bodies after collision is equal to the relative speed before the collision.

Statement 2 :

In an elastic collision, the linear momentum of the system is conserved.

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