A bob of mass m suspended by a thread of length ℓ undergoes simple harmonic oscillations with time period T. If the bob is immersed in a liquid that has density 14 times that of the bob and the length of the thread is increased by 13rd of the original length, then the new time period of the oscillations will be:

In an open organ pipe, v3 and v6 are the 3rd and 6th harmonic frequencies, respectively. If v6 − v3 = 2200 Hz, then the length of the pipe is ______ mm. (Take velocity of sound in air as 330 m/s.)

There is a second's pendulum on the surface of the earth. It is taken to the surface of a planet whose mass and radius are twice that of the earth. The period of oscillation of this second's pendulum on the planet will be: