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.

When a body slides down from rest along a smooth inclined plane making an angle of 45^o with the horizontal, it takes time T. when the same body slides down from rest along a rough inclined plane making the same angle and through the same distance, it is seen to taken time pT, where p is some number greater than 1. Calculate the coefficient of friction between the body and the rough plane.

(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?

A balloon has 5.0 g mole of helium at 7°C. Calculate
(i) the number of atoms of helium in the balloon.
(ii) the total internal energy of the system.

Ten small planes are flying at a speed of 150 km/h in total darkness in an air space that is 20 x 20 x 1.5 km³ in volume. You are in one of the planes, flying at random within the space with no way of knowing where the other planes are. On the average about how long a time will elapse between near collision with you plane. Assume for this rough computation that a safety region around the plane can be approximated by a sphere of radius 10 m.

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 \(\frac { \lambda }{2 } \).

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 What is the phase difference between the oscillation of a particle located at x=100 cm, at t=Ts and t = 5s?

In the given progressive wave
y=5sin(100πt−0.4πx) where y and x are in m,t is in s.
A: What is the amplitude and wavelength?
B: What is the frequency and wave velocity? (Wavelength is 5 m)
C: What is the particle velocity amplitude?

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.

A motor car moving at a speed of 72 km/h cannot come to a stop is less than 3.0 s while for a truck time interval is 5.0 s. On a highway, the car is behind the truck both moving at 72 krn/h. The truck gives a signal that it is going to stop at emergency. At what distance the car should be from the truck so that it does not bumb onto (collide with) the truck? Human response time is 0.5 s