If the angular momentum of a planet of mass m, moving around the Sun in a circular orbit is L, about the center of the Sun, its areal velocity is :

Two masses m and $${m \over 2}$$ are connected at the two ends of a massless rigid rod of length l. The rod is suspended by a thin wire of torsional constant k, at the centre of mass of the rod-mass system(see figure). Because of torsional constant k, the restoring torque is $$\tau $$ = k$$\theta $$ for angular displacement $$\theta $$. If the rod is rotated by $$\theta $$₀ and released, the tension in it when it passes through its mean position will be :

A conducting circular loop made of a thin wire, has area 3.5 $$ \times $$ 10^$$-$$3 m² and resistance 10 $$\Omega $$. It is placed perpendicular to a time dependent magnetic field B(t) = (0.4T)sin(50$$\pi $$t). The field is uniform in space. Then the net charge flowing through the loop during t = 0 s and t = 10 ms is close to :

A block of mass m, lying on a smooth horizontal surface, is attached to a sring (of negligible mass) of spring constant k. The other end of the spring is fixed, as shown in the figure. The block is initially at rest in its equilibrium position. If now the block is pulled with a constant force F, the maximum speed of the block is :