**Answer in brief:**

Why are curved roads banked?

Concept: Rotational Dynamics

**Answer in brief:**

On what factors does the frequency of a conical pendulum depend? Is it independent of some factors?

Concept: Rotational Dynamics

While driving along an unbanked circular road, a two-wheeler rider has to lean with the vertical. Why is it so? With what angle the rider has to lean? Derive the relevant expression. Why such a leaning is not necessary for a four wheeler?

Concept: Rotational Dynamics

Somehow, an ant is stuck to the rim of a bicycle wheel of diameter 1 m. While the bicycle is on a central stand, the wheel is set into rotation and it attains the frequency of 2 rev/s in 10 seconds, with uniform angular acceleration. Calculate:

(i) The number of revolutions completed by the ant in these 10 seconds.

(ii) Time is taken by it for first complete revolution and the last complete revolution.

Concept: Rotational Dynamics

The coefficient of static friction between a coin and a gramophone disc is 0.5. Radius of the disc is 8 cm. Initially the center of the coin is π cm away from the center of the disc. At what minimum frequency will it start slipping from there? By what factor will the answer change if the coin is almost at the rim?

(use g = π^{2}m/s^{2})

Concept: Rotational Dynamics

**Answer in Brief:**

A flywheel used to prepare earthenware pots is set into rotation at 100 rpm. It is in the form of a disc of mass 10 kg and a radius 0.4 m. A lump of clay (to be taken equivalent to a particle) of mass 1.6 kg falls on it and adheres to it at a certain distance x from the center. Calculate x if the wheel now rotates at 80 rpm.

Concept: Rotational Dynamics

Starting from rest, an object rolls down along an incline that rises by 3 in every 5 (along with it). The object gains a speed of `sqrt10` m/s as it travels a distance of `5/3` m along the incline. What can be the possible shape/s of the object?

Concept: Rotational Dynamics

**Multiple Choice Question.**

Two capillary tubes of radii 0.3 cm and 0.6 cm are dipped in the same liquid. The ratio of heights through which the liquid will rise in the tubes is

Concept: Fluid and Its Properties

Why is a low-density liquid used as a manometric liquid in a physics laboratory?

Concept: Fluid and Its Properties

What is an incompressible fluid?

Concept: Fluid and Its Properties

Obtain an expression for conservation of mass starting from the equation of continuity.

Concept: Fluid and Its Properties

The speed of water is 2m/s through a pipe of internal diameter 10 cm. What should be the internal diameter of the nozzle of the pipe if the speed of the water at nozzle is 4 m/s?

Concept: Fluid and Its Properties

With what velocity does water flow out of an orifice in a tank with gauge pressure 4 × 10^{5} N/m^{2} before the flow starts? Density of water = 1000 kg/m^{3}.

Concept: Fluid and Its Properties

A big dumb-bell is prepared by using a uniform rod of mass 60 g and length 20 cm. Two identical solid spheres of mass 50 g and radius 10 cm each are at the two ends of the rod. Calculate the moment of inertia of the dumb-bell when rotated about an axis passing through its centre and perpendicular to the length.

Concept: Rotational Dynamics

Why two or more mercury drops form a single drop when brought in contact with each other?

Concept: Fluid and Its Properties

The pressure of water inside a closed pipe is 3 × 10^{5} N/m^{2}. This pressure reduces to 2 × 10^{5} N/m^{2} on opening the valve of the pipe. Calculate the speed of water flowing through the pipe. [Density of water = 1000 kg/m^{3}].

Concept: Fluid and Its Properties

How much work is required to form a bubble of 2 cm radius from the soap solution having surface tension 0.07 N/m?

Concept: Fluid and Its Properties

A rectangular wireframe of size 2 cm x 2 cm, is dipped in a soap solution and taken out. A soap film is formed, it the size of the film is changed to 3 cm x 3 cm, Calculate the work done in the process. The surface tension of the soap film is 3 x 10^{-2} N/m.

Concept: Fluid and Its Properties

Unit of the coefficient of viscosity is ______

Concept: Fluid and Its Properties

Two capillary tubes of radii 0.6 cm and 0.3 cm are dipped in the same liquid. The ratio of heights through which the liquid will rise in the tubes is ______

Concept: Fluid and Its Properties