When a string of length '$$l$$' is divided into three segments of length $$l_1, l_2$$ and $$l_3$$. The fundamental frequencies of three segments are $$\mathrm{n}_1, \mathrm{n}_2$$ and $$\mathrm{n}_3$$ respectively. The original fundamental frequency '$$n$$' of the string is

A seconds pendulum is placed in a space laboratory orbiting round the earth at a height '$$3 \mathrm{R}$$' from the earth's surface. The time period of the pendulum will be ( $$R=$$ radius of earth)

A solid metallic sphere has a charge $$+3 Q$$. Concentric with this sphere is a conducting spherical shell having charge $$-\mathrm{Q}$$. The radius of the sphere is '$$A$$' and that of the spherical shell is '$$B$$'. $$(B > A)$$. The electric field at a distance '$$\mathrm{R}$$' $$(\mathrm{A} < \mathrm{R} < \mathrm{B})$$ from the centre is ( $$\varepsilon_0=$$ permittivity of vacuum)

A closed organ pipe of length '$$L_1$$' and an open organ pipe contain diatomic gases of densities '$$\rho_1$$' and '$$\rho_2$$' respectively. The compressibilities of the gases are same in both pipes, which are vibrating in their first overtone with same frequency. The length of the open organ pipe is (Neglect end correction)