It is a common observation that rain clouds can be at about a kilometre altitude above the ground.
(a) If a rain drop falls from such a height freely under gravity, what will be its speed?Also, calculate in km/h (g = 10 m/s²).
(b) A typical rain drop is about 4 mm diameter.Momentum is mass x speed in magnitude.Estimate its momentum when it hits ground.
(c) Estimate time required to flatten the drop.
(d) Rate of change of momentum is force.Estimate how much force such a drop would exert on you?
(e) Estimate the order of magnitude force on umbrella. Typical lateral separation between two rain drops is 5cm.

A girl riding a bicycle along a straight road with a speed of 5 m/ s throws a stone of mass 0.5 kg which has a speed of 15 m /s with respect to the ground along her direction of motion. The mass of the girl and bicycle is 50 kg. Does the speed of the bicycle change after the stone is thrown ? What is the change in speed, if so ?

Figure shows (x, t), (y, t) diagram of a particle moving in 2-dimensions.
 
If the particle has a mass of 500 g, find the force (direction and magnitude) acting on the particle.

(a) A child stands at the centre of a turntable with his two arms outstretched. The turntable is set rotating with an angular speed of 40 rev/min. How much is the angular speed of the child if he folds his hands back and thereby reduces his moment of inertia to 2/5 times the initial value ? Assume that the turntable rotates without friction.
(b) Show that the child’s new kinetic energy of rotation is more than the initial kinetic energy of rotation. How do you account for this increase in kinetic energy?

The Young's modulus for stell is much more than that for rubber. For the same longitudinal strain, which one will have greater tensile stress?

Consider a Carnot cycle operating between T₁ = 500K and T₂ = 300K producing 1KJ of mechanical work per cycle. Find the heat transferred to/by the engine by/to the reservoir.

A gas mixture consists of 2.0 moles of oxygen and 4.0 moles of neon at temperature T. Neglecting all vibrational modes, calculate the total internal energy of the system. (oxygen has two rotational modes)

For the harmonic travelling wave  \(y=2\cos { 2\pi } \left( 10t-0.0080x+3.5 \right) \) , where, x and y are in cm and t is in second. What is the phase difference between the oscillatory motion at two points separated by a distance of \(\frac { 3\lambda }{ 4 } \)(at a given instant in time)?

A solid sphere rolls down two different inclined planes of the same heights but different angles of inclination.
(a) Will it reach the bottom with the same speed in each case?
(b) Will it take longer to roll down one plane than the other?
(c) If so, which one and why?

The oxygen molecule has a mass of 5.30 × 10^-26 kg and a moment of inertia of 1.94 × 10^-46 kg m² about an axis through its centre perpendicular to the lines joining the two atoms. Suppose the mean speed of such a molecule in a gas is 500 m/s and that its kinetic energy of rotation is two thirds of its kinetic energy of translation. Find the average angular velocity of the molecule.