PART - 1 CH - 1 Units and Measurements — Physics STD 11 Science — Question

Find the components along the x, y, z axes of the angular momentum l of a particle, whose position vector is r with components x, y, z and momentum is p with components px, py and pz. Show that if the particle moves only in the x-y plane the angular momentum has only a z-component.

The position, velocity and acceleration of a particle executing simple harmonic motion are found to have magnitudes 2cm, 1m/s and 10m/s² at a certain instant. Find the amplitude and the time period of the motion.

Ten small planes are flying at a speed of 150km/h in total darkness in an air space that is 20 × 20 × 1.5km 3 in volume. You are in one of the planes, flying at random within this 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 your plane. Assume for this rough computation that a safety region around the plane can be approximated by a sphere of radius 10m.

Io, one of the satellites of Jupiter, has an orbital period of 1.769 days and the radius of the orbit is 4.22 × 10⁸m. Show that the mass of Jupiter is about one-thousandth that of the sun.

A quarterback, standing on his opponents 35-yard line, throws a football directly down field, releasing the ball at a height of 2.00m above the ground with an initial velocity of 20.0m/ s, directed 30.0° above the horizontal.

1. How long does it take for the ball to cross the goal line, 32.0m from the point of release?
2. The ball is thrown too hard and so passes over the head of the intended receiver at the goal line. What is the ball's height above the ground as it crosses the goal line?

What are the characteristics of stationary waves? Distinguish between stationary waves and progressive waves.

A 3m long ladder weighing 20 kg leans on a frictionless wall. Its feet rest on the floor 1 m from the wall as shown in Fig.6.27. Find the reaction forces of the wall and the floor.

If the earth were a homogeneous sphere and a straight hole bored in it through its centre, show that if a body were dropped into the hole it would execute a simple harmonic motion. Also find its time period.

A block of mass 2.0kg is pushed down an inclined plane of inclination 37° with a force of 20N acting parallel to the incline. It is found that the block moves on the incline with an acceleration of 10m/s². If the block started from rest, find the work done.

1. By the applied force in the first second.
2. By the weight of the block in the first second.
3. By the frictional force acting on the block in the first second. Take g = 10m/s².