Author: Physics Notebook

Find The Value Of Position Vector In Two-Dimensional And Three-Dimensional Cartesian Co-Ordinate System.

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Physics Notebook

Position vector in two-dimensional cartesian co-ordinate system: A particle is moving in a plane so we will use a two-dimensional co-ordinate system in this case to describe the motion of the particle. Let us consider the motion in X-Y plane. Let at any instant of time and be the Cartesian co-ordinates of the particle P.…
Derive The Relation Between Three Dimensional Cartesian Co-ordinates And The Spherical Polar Co-ordinates.

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Physics Notebook

Relation between polar co-ordinates and three-dimensional Cartesian co-ordinates: Let us consider, x, y, and z to be the Cartesian co-ordinates of the point A as shown in the adjoining figure. OB is the projection of OA in the X-Y plane, since OA makes an angle with the positive Z-axis, so . Since is the azimuthal…
What Is Spherical Polar Co-Ordinate System? What Are Their Limits?

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Physics Notebook

Spherical polar co-ordinate: The spherical polar co-ordinate system is a method of representation, which helps to represent the co-ordinates of a point on the surface of a sphere. There are three co-ordinates in this system. The three co-ordinates for a point A in the spherical polar co-ordinate system are given bellow: The radial distance of…
What Is The Plane Polar Co-Ordinate System?

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Physics Notebook

Plane polar co-ordinate system: In the study of two-dimensional cases, we observe the motion takes place in a plane. Sometimes the plane polar co-ordinate is very suitable for this purpose. In this plane polar co-ordinate system, the two co-ordinates for a point are: (i) r is the radial distance of the point A from the…
What Is Rectangular Cartesian Co-Ordinates System?

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Physics Notebook

Rectangular cartesian co-ordinate system: In classical mechanics, it is considered that there are three dimensions in space. These three dimensions are represented by three axes in the cartesian co-ordinate system. These three axes are X-axis, Y-axis and Z-axis, which are mutually perpendicular to each other. The origin is denoted by the fixed point where these…
A Particle Is Dropped Vertically On To A Fixed Horizontal Plane From Rest At A Height ‘H’ From The Plane. Calculate The Total Theoretical Time Taken By The Particle To Come To Rest.

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Physics Notebook

Ans. A particle is dropped vertically on a fixed horizontal plane from a height above the plane.At height the particle is at rest, i.e., the initial velocity of the particle is zero. Let be the velocity of the particle just before the collision with the plane and be the velocity just after the particle hits the…
A Particle Dropped Vertically On A Fixed Horizontal Plane From Rest At A Height ‘H’ Above The Plane. Calculate The Total Theoretical Distance Traveled By The Particle Before Coming To Rest.

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Physics Notebook

Ans. A particle is dropped vertically on a fixed horizontal plane from a height above the plane.At height the particle is at rest, i.e., the initial velocity of the particle is zero. Let be the velocity of the particle just before the collision with the plane and be the velocity just after the particle hits…
A Particle Is Dropped Vertically On To A Fixed Horizontal Plane. If It Hits The Plane With Velocity ‘u’, Show That It Rebounds With Velocity (-eu).

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Physics Notebook

Ans. Let be the velocity of the particle after collision with the horizontal plane. is the velocity of the particle before collision with the horizontal plane. If be the coefficient of restitution, then or, or, Since the direction of the velocity is opposite to the direction of . So .
A Particle Of Mass ‘m’ Moving With Velocity ‘u’ Collides With A Target Particle Of Unknown Mass Initially At Rest. If After The Collision The Target Particles Travels Forward With A Velocity ‘u/3’, While The Incident Particle Moves Backward With A Velocity ‘2u/3’, Find The Mass Of The Target Particle.

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Physics Notebook

Ans. A particle of mass moving with velocity collides with a particle at rest.Let us consider, be the velocity of the target particle. After collision, the target particle moves forward with velocity and the incident particles moves backward with velocity According to the conservation of linear momentum, or, or, or, or, So the mass of…
A Gun Fires A Bullet Of Mass ‘m’ With Horizontal Velocity ‘v’ Into A Block Of Wood Of Mass ‘M’ Which Rest At A Horizontal Friction Less Plane, If The Bullet Becomes Embedded In The Wood, (i) Determine The Subsequent Velocity Of The System And (ii) Find The Loss In The Kinetic Energy.

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Physics Notebook

Ans. The masses of the bullet and the block of wood are and respectively. The velocity of the bullet before collision is . Since the wood block is at rest, so the velocity of the wood block before collision is Zero. After collision the bullet becomes embedded in the wood block. (i) Subsequent velocity of…