A pipe open at both ends has a fundamental frequency f in air. The pipe is now dipped vertically in a water drum to half of its length. The fundamental frequency of the air column is now equal to:
An oxygen cylinder of volume 30 litre has 18.20 moles of oxygen. After some oxygen is withdrawn from the cylinder, its gauge pressure drops to 11 atmospheric pressure at temperature $27^{\circ}C.$ The mass of the oxygen withdrawn from the cylinder is nearly equal to:[Given, $R=\frac{100}{12}Jmol^{-1}K^{-1},$ and molecular mass of $O_{2}=32$, 1 atm pressure $=1.01\times10^{5}N/m^{2}$]
A particle of mass m is moving around the origin with a constant force F pulling it towards the origin. If Bohr model is used to describe its motion, the radius of the $n^{th}$ orbit and the particle’s speed v in the orbit depend on n as
In some appropriate units, time (t) and position (x) relation of a moving particle is given by $t=x^{2}+x$ The acceleration of the particle is
The radius of Martian orbit around the Sun is about 4 times the radius of the orbit of Mercury. The Martian year is 687 Earth days. Then which of the following is the length of 1 year on Mercury?