A cylindrical tube, open at both ends, has a fundamental frequency, f, in the air. The tube is dipped vertically in water so that half of it is in water. The fundamental frequency of the air-column is now

• m₁r₁:m₂r₂

• m₁ :m₂

• r₁ :r₂

• r₁ :r₂

A thin horizontal circular disc is rotating about a vertical axis passing through its centre. An insect is at rest at a point near the rim of the disc. The insect now moves along a diameter of the disc to reach its other end. During the journey of the insect, the angular speed of the disc 

• remains unchanged

• continuously decreases

• continuously increases 

• continuously increases 

A hoop of radius r and mass m rotating with an angular velocity ω₀
is placed on a rough horizontal surface.The initial velocity of the centre of the hoop is zero. What will be the velocity of the centre of the hoop when it ceases to slip?

• rω₀/4

• rω₀/3

• rω₀/2

• rω₀/2

Two identical charged spheres suspended from a common point by two massless strings of length l are initially a distance d(d < < l) apart because of their mutual repulsion. The charge begins to leak from both the spheres at a constant rate.As a result the charges approach each other with a velocity v. Then as a function of distance x between them

• v ∝ x^-1

• v ∝ x^1/2

• v ∝ x

• v ∝ x

A diatomic molecule is made of two masses m₁ and m₂ which are separated by a distance r. If we calculate its rotational energy by applying Bohr's rule of angular momentum quantization, its energy will be given by (n is an integer)