The fundamental frequency of a closed organ pipe is equal to the first overtone frequency of an open organ pipe. If length of the open pipe is $$60 \mathrm{~cm}$$, the length of the closed pipe will be:

If the wavelength of the first member of Lyman series of hydrogen is $$\lambda$$. The wavelength of the second member will be

A coil is places perpendicular to a magnetic field of $$5000 \mathrm{~T}$$. When the field is changed to $$3000 \mathrm{~T}$$ in $$2 \mathrm{~s}$$, an induced emf of $$22 \mathrm{~V}$$ is produced in the coil. If the diameter of the coil is $$0.02 \mathrm{~m}$$, then the number of turns in the coil is:

A coin is placed on a disc. The coefficient of friction between the coin and the disc is $$\mu$$. If the distance of the coin from the center of the disc is $$r$$, the maximum angular velocity which can be given to the disc, so that the coin does not slip away, is :