A particle of mass '$$m$$' moving east ward with a speed '$$v$$' collides with another particle of same mass moving north-ward with same speed '$$v$$'. The two particles coalesce after collision. The new particle of mass '$$2 \mathrm{~m}$$' will move in north east direction with a speed (in $$\mathrm{m} / \mathrm{s}$$ )

The height at which the weight of the body becomes $$\left(\frac{1}{9}\right)^{\text {th }}$$ its weight on the surface of earth is $$(\mathrm{R}=$$ radius of earth)

A single turn current loop in the shape of a right angle triangle with side $$5 \mathrm{~cm}, 12 \mathrm{~cm}, 13 \mathrm{~cm}$$ is carrying a current of $$2 \mathrm{~A}$$. The loop is in a uniform magnetic field of magnitude $$0.75 \mathrm{~T}$$ whose direction is parallel to the current in the $$13 \mathrm{~cm}$$ side of the loop. The magnitude of the magnetic force on the $$5 \mathrm{~cm}$$ side will be $$\frac{\mathrm{x}}{130} \mathrm{~N}$$. The value of '$$x$$' is

41 tuning forks are arranged in increasing order of frequency such that each produces 5 beats/second with next tuning fork. If frequency of last tuning fork is double that of frequency of first fork. Then frequency of first and last fork is