A block $$M$$ hangs vertically at the bottom end of a uniform rope of constant mass per unit length. The top end of the rope is attached to fixed rigid support at $$O.$$ A transverse wave pulse (Pulse 1) of wavelength $${\lambda _0}$$ is produced at point $$O$$ on the rope. The pulse takes time $${T_{OA}}$$ to reach point $$A.$$ If the wave pulse of wavelength $${\lambda _0}$$ is produced at point $$A$$ (Pulse 2) without disturbing the position of $$M$$ it takes time $${T_{AO}}$$ to reach point $$O.$$ which of the following options is/are correct?

A block of mass $$M$$ has a circular cut with a frictionless surface as shown. The block resets on the horizontal frictionless surface of a fixed table. Initially the right edge of the block is at $$x=0,$$ in a co-ordinate system fixed to the table. A point mass $$m$$ is released from rest at the topmost point of the path as shown and it slides down.

When the mass loses contact with the block, its position is $$x$$ and the velocity is $$v.$$ At that instant, which of the following options is/are correct?

A human body has a surface area of approximately $$1\,m{}^2.$$ The normal body temperature is $$10$$ $$K$$ above the surrounding room temperature $${T_0}.$$ Take the room temperature to be $${T_0} = 300K.$$ For $${T_0} = 300\,K,$$ the value of $$\sigma T_0^4 = 460\,W{m^{ - 2}}$$ (where $$\sigma $$ is the Stefan-Boltzmann constant).

Which of the following options is / are correct?

A circular insulated copper wire loop is twisted to form two loops of area $$A$$ and $$2A$$ as shown in the figure. At the point of crossing the wires remain electrically insulated from each other. The entire loop lies in the plane (of the paper). A uniform magnetic field $$\overrightarrow B $$ points into the plane of the paper. At $$t=0,$$ the loop starts rotating about the common diameter as axis with a constant angular velocity $$\omega $$ in the magnetic field.

Which of the following options is/are correct?