To simulate car accidents, auto manufacturers study the collisions of moving cars with mounted springs of different spring constants. Consider a typical simulation with a car of mass 1000 kg moving with a speed 18.0 km/h on a smooth road and colliding with a horizontally mounted spring of spring constant 5.25 × 10^3 N m–1. What is the maximum compression of the spring ? Example 5.9 Consider Example 5.8 taking the coefficient of friction, µ, to be 0.5 and calculate the maximum compression of the spring.

Example 5.8 To simulate car accidents, auto manufacturers study the collisions of moving cars with mounted springs of different spring constants. Consider a typical simulation with a car of mass 1000 kg moving with a speed 18.0 km/h on a smooth road and colliding with a horizontally mounted spring of spring constant $5.25\times 10^3 Nm^{-1}$ . What is the maximum compression of the spring ? [NCERT Class 11 Example 5.8]

Example 5.9 Consider Example 5.8 taking the coefficient of friction, µ, to be 0.5 and calculate the maximum compression of the spring. [NCERT Class 11 Example 5.9]

$5.25\times 10^3 Nm^{-1}$ corrected as $6.25\times 10^3 Nm^{-1}$

Three concentric spherical shells have radii a, b and c (a < b < c) and have surface charge densities σ,−σ and σ respectively. If VA, VB and VC denotes the potentials of the three shells, then for c = a + b, we have [NEET 2009]

Three concentric spherical shells have radii a, b and c (a < b < c) and have surface charge densities σ,−σ and σ respectively. If VA, VB and VC denotes the potentials of the three shells, then for c = a + b, we have [NEET 2009]

a) $V_C=V_B\neq V_A$

b) $V_C\neq V_B\neq V_A$

c) $V_C=V_B=V_A$

d) $V_C=V_A\neq V_B$

Concept: Use Van de graph principles. In concentric spheres, the voltage due to the charges on the surface and the voltage due to the inner spheres and outer spheres should be added. $V_{inside\hspace{2mm}sphere}= V_{at\hspace{2mm}surface\hspace{2mm}of\hspace{2mm}sphere}$

\[V_A=\frac{1}{4\pi\epsilon_o}\frac{q_A}{r_A}-\frac{1}{4\pi\epsilon_o}\frac{q_B}{r_B}+\frac{1}{4\pi\epsilon_o}\frac{q_C}{r_C}\]

\[=K\frac{\sigma 4\pi a^2}{a}-K\frac{\sigma 4\pi b^2}{b}+K\frac{\sigma 4\pi c^2}{c}\]

\[=K\sigma 4\pi \hspace{2mm}(a-b+c)\]

\[=K\sigma 4\pi \hspace{2mm}(a-b+a+b)\]

\[=K \sigma 4\pi \hspace{2mm} (2a) \]

A man of 50 kg mass is standing in a gravity free space at a height of 10 m above the floor. He throws a stone of 0.5 kg mass downwards with a speed of 2 m/s. When the stone reaches the floor the distance of the man above the floor will be

A man of 50 kg mass is standing in a gravity free space at a height of 10 m above the floor. He throws a stone of 0.5 kg mass downwards with a speed of 2 m/s. When the stone reaches the floor the distance of the man above the floor will be

A) 9.9 m   B) 10.1 m  C) 10 m   D) 20 m

Concepts: Conservation of Linear momentum. Similar to the recoiling of gun. When the man pushes the stone downward the man will get pushed upward. Since there is no external force acting on the system, conservation of linear momentum is valid and center of mass of the whole system remains in the same location.

12P01 Electric Charges and Fields

 Step-by-step

Step 1: Theory and Concepts

NCERT Text book, Handbook Study notes

Step 2: Numerical Practice

NCERT Examples, NCERT Exercises with solutions

Step 3: Numerical Practice

Chapterwise CBSE Past papers (Any one of them- Arihant, MTG, XAM Idea etc.)

Step 4: Numerical Practice

NCERT competency based questions 2024, Solutions

NCERT competency based questions 2023, Solutions

Step 5: Numerical Practice

NCERT Exemplar Questions, Solutions

NEET past year Questions, Solutions

JEE Main past year Questions, Solutions

Two charges and Forces between them.

Plot F vs. r graph to see the shape of the graph.

How to solve Numerical problem in physics?

 

How to solve Numerical problem in physics?

“Start walking. The path will become clearer”

 Step 1: Translating from English language to Maths and Drawing.

·        Nature is written in the language of Mathematics. Drawing is the language of Engineers and Scientists.

·        Read the question line by line converting it into a simple cartoon diagram or a mathematical expression. Mark the numerical values in appropriate places in the diagram or with the mathematical notations.

 Step 2: Understand what is given and what is to be found.

Charged Particle in a Uniform Electric Field. Calculate the vertical distance from the center line from where the particle will exit the parallel plate region.

 

Charged Particle in a Uniform Electric Field

Calculate the vertical distance from the center line 

from where the particle will exit the parallel plate region.