SATHEE: Study Material

Shortcut Methods

1. Conservation of Momentum:

Problem: A 10 kg ball moving at 5 m/s collides elastically with a stationary 15 kg ball. Find the velocities of both balls after the collision.
Solution:
- Shortcut: Use the concept of relative velocity. This is the difference in velocities between the two balls before the collision.
- Formula: Relative velocity = velocity of ball 1 - velocity of ball 2
- In this case, the relative velocity is 5 m/s - 0 m/s = 5 m/s.

January 1, 0001 read

Shortcut Methods

1. Two Objects Colliding:

Initial momentums: (p_1 = m_1v_1) and (p_2 = m_2v_2)

Final momentum (after collision): (p_f = (m_1 + m_2)v)

Using conservation of momentum: $$p_1 + p_2 = p_f $$ $$m_1v_1 + m_2v_2 = (m_1 + m_2)v$$ $$v = \frac{m_1v_1 + m_2v_2}{m_1 + m_2}$$

2. Ball Colliding with a Wall

Impulse: (J = \Delta p)

Initial momentum: (p_i = mv)

Final momentum: (p_f = -mv) (negative sign due to the change in direction)

January 1, 0001 read

Shortcut Methods

Numerical 1:

Solution:
- Work done = Force * Distance moved in the direction of the force
- In this case, the block is moved vertically upward, against the force of gravity.
- Therefore, the work done by the force of gravity is negative.

Numerical 2:

Solution:
- The potential energy stored in a spring is equal to the work done in stretching or compressing the spring.
- In this case, the work done in stretching the spring is equal to the potential energy stored in the spring.

Numerical 3:

Solution:
- The maximum height reached by a projectile is equal to the square of its initial velocity divided by twice the acceleration due to gravity.
- In this case, the initial velocity of the ball is 10 m/s and the acceleration due to gravity is -9.8 m/s^2.

January 1, 0001 read

Structural-Organization-Morphology-Of-Plants-3

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Structural-Organizationstructural-Organization-In-Animals-2

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January 1, 0001 read

Superposition Principle For Electrostatic Force

1. Coulomb’s Law

The electrostatic force between two point charges $q_1$ and $q_2$ separated by a distance $r$ is given by:

$$F = k\frac{|q_1q_2|}{r^2}$$

where $k$ is the Coulomb constant.

NCERT Reference: NCERT Class 12, Chapter-1: Electric Charges and Fields

2. Electric Field

The electric field $\overrightarrow{E}$ at a point due to a point charge $q$ is given by the formula:

$$\overrightarrow{E} = k\frac{q}{r^2}\hat{r}$$

where $\hat{r}$ is the unit vector pointing away from the source charge.

January 1, 0001 read

Three Dimensional Geometry

Lines and Planes

Equations of lines and planes in space:

Use parametric equations to represent lines.
Use the vector equation of a plane to represent planes.

Angle between two lines and between a line and a plane:

Use the dot product of two vectors to find the angle between them.
Use the angle between a line and a plane to find the shortest distance from the line to the plane.

Distance from a point to a line and from a point to a plane:

Use the perpendicular distance formula to find the distance from a point to a line or a plane.

Spheres

January 1, 0001 read

Unit 10 Haloalkanes And Haloarenes (Exercises)

Exercises

10.1 Name the following halides according to IUPAC system and classify them as alkyl, allyl, benzyl (primary, secondary, tertiary), vinyl or aryl halides:

(i) $\left({CH_3}\right)_{2} {CHCH}({Cl}) {CH_3}$

(ii) ${CH_3} {CH_2} {CH}\left({CH_3}\right) {CH}\left({C_2} {H_5}\right) {Cl}$

(iii) ${CH_3} {CH_2} {C}\left({CH_3}\right)_{2} {CH_2} {I}$

(iv) $\left({CH_3}\right)_{3} {CCH_2} {CH}({Br}) {C_6} {H_5}$

(v) ${CH_3} {CH}\left({CH_3}\right) {CH}({Br}) {CH_3}$

(vi) ${CH_3} {C}\left({C_2} {H_5}\right)_{2} {CH_2} {Br}$

(vii) ${CH_3} {C}({Cl})\left({C_2} {H_5}\right) {CH_2} {CH_3}$

(viii) ${CH_3} {CH}={C}({Cl}) {CH_2} {CH}\left({CH_3}\right)_{2}$

January 1, 0001 read

Unit 11 Alcohols, Phenols And Ethers (Intext Questions-3)

Intext Questions

11.4 Show how are the following alcohols prepared by the reaction of a suitable Grignard reagent on methanal?

Show Answer

Answer

(i)

(ii)

11.5 Write structures of the products of the following reactions:

Show Answer

Answer

January 1, 0001 read

Unit 11 Alcohols, Phenols And Ethers (Intext Questions-4)

Intext Questions

11.6 Give structures of the products you would expect when each of the following alcohol reacts with (a) ${HCl}-{ZnCl_2}$ (b) ${HBr}$ and (c) ${SOCl_2}$.

(i) Butan-1-ol

(ii) 2-Methylbutan-2-ol

Show Answer

Answer

(a)

(i) $\underset{\text{Butan-1-ol}}{{CH_3}-{CH_2}-{CH_2}-{CH_2}-{OH}} \xrightarrow{{HCl} - {ZnCl_2}} \text { No reaction }$

Primary alcohols do not react appreciably with Lucas’ reagent $\left({HCl}-{ZnCl_2}\right)$ at room temperature.

(ii)

Tertiary alcohols react immediately with Lucas’ reagent

(b)

(i) $\underset{\text{Butan-1-ol}}{{CH_3} {CH_2} {CH_2} {CH_2} {OH}}+{HBr} \xrightarrow{{-H_2O}}\underset{\text{1-Bromobutane}}{{CH_3} {CH_2} {CH_2} {CH_2} {Br}}$

January 1, 0001 read

Unit 7 The P Block Elements (Intext Questions-14)

January 1, 0001 read

Shortcut Methods

1. Two Objects Colliding:

2. Ball Colliding with a Wall

Shortcut Methods

Numerical 1:

Numerical 2:

Numerical 3:

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Unit 10 Haloalkanes And Haloarenes (Exercises)

Exercises

Unit 11 Alcohols, Phenols And Ethers (Intext Questions-3)

Intext Questions

Unit 11 Alcohols, Phenols And Ethers (Intext Questions-4)

Intext Questions

Shortcut Methods

Structural-Organization-Morphology-Of-Plants-3

Structural-Organizationstructural-Organization-In-Animals-2

Superposition Principle For Electrostatic Force

Three Dimensional Geometry

Unit 7 The P Block Elements (Intext Questions-14)

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Mentorship

NCERT Exercise Video Solution

Forum

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Shortcut Methods

Shortcut Methods

1. Two Objects Colliding:#

2. Ball Colliding with a Wall#

Shortcut Methods

Numerical 1:#

Numerical 2:#

Numerical 3:#

Structural-Organization-Morphology-Of-Plants-3

Structural-Organizationstructural-Organization-In-Animals-2

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Superposition Principle For Electrostatic Force

Three Dimensional Geometry

Unit 10 Haloalkanes And Haloarenes (Exercises)

Exercises#

Unit 11 Alcohols, Phenols And Ethers (Intext Questions-3)

Intext Questions#

Unit 11 Alcohols, Phenols And Ethers (Intext Questions-4)

Intext Questions#

Unit 7 The P Block Elements (Intext Questions-14)

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Mentorship

NCERT Exercise Video Solution

Forum

For International Students

Get In Touch

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1. Two Objects Colliding:

2. Ball Colliding with a Wall

Numerical 1:

Numerical 2:

Numerical 3:

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Exercises

Intext Questions

Intext Questions