The mass of earth is 81 times the mass of the moon and the distance between their centres is $$R$$. The distance from the centre of the earth, where gravitational force will be zero is

A coil of $$n$$ turns and resistance $$R \Omega$$ is connected in series with a resistance $$\frac{R}{2}$$. The combination is moved for time $$t$$ second through magnetic flux $$\phi_1$$ to $$\phi_2$$. The induced current in the circuit is

Two identical bar magnets each of magnetic moment $$M$$, separated by some distance are kept perpendicular to each other. The magnetic induction at a point at the same distance $$d$$ from the centre of magnets, is ($$\mu_0=$$ permeability of free space)

A bullet of mass $$m$$ moving with velocity $$v$$ is fired into a wooden block of mass $$M$$, If the bullet remains embedded in the block, the final velocity of the system is