A metallic sphere cools from 50^oC to 40^o in 300 s. If atmospheric temperature around is 20^oC, then the sphere’s temperature after the next 5 minutes will be close to :

A block of mass 1.9 kg is at rest at the edge of a table, of height 1 m. A bullet of mass 0.1 kg collides with the block and sticks to it. If the velocity of the bullet is 20 m/s in the horizontal direction just before the collision then the kinetic energy just before the combined system strikes the floor, is [Take g = 10 m/s² . Assume there is no rotational motion and loss of energy after the collision is negligable.]

The radius R of a nucleus of mass number A can be estimated by the formula
R = (1.3 $$ \times $$ 10^–15)A^1/3 m.
It follows that the mass density of a nucleus is of the order of :

(M_prot. $$ \cong $$ M_neut $$ \simeq $$ 1.67 $$ \times $$ 10^–27 kg)

A uniform magnetic field B exists in a direction perpendicular to the plane of a square loop made of a metal wire. The wire has a diameter of 4 mm and a total length of 30 cm. The magnetic field changes with time at a steady rate $${{dB} \over {dt}}$$ = 0.032 Ts^–1. The induced current in the loop is close to (Resistivity of the metal wire is 1.23 $$ \times $$ 10^–8 $$\Omega $$m)