Maharashtra State Board 11th Physics Solutions Chapter 2 Mathematical Methods
1. Choose the correct option.
Solution & Step-by-Step Answer:
(D) 5 N along – x-axis
Solution & Step-by-Step Answer:
(C) same magnitude and direction
Solution & Step-by-Step Answer:
(A) zero
Solution & Step-by-Step Answer:
(D)
Solution & Step-by-Step Answer:
(C) × = ×
2. Answer the following questions.
Solution & Step-by-Step Answer:
Solution & Step-by-Step Answer:
+ = (3 + 4 + ) + ( – – ) = 3 + 3 + 4 – + – = 4 + 3 ∴ Magnitude of ( + ), | + | = = = 5 units. Answer: Magnitude of + = 5 units.
Solution & Step-by-Step Answer:
+ = (2 – 3) + (-6 + 5) = (2 – 6) + (-3 + 5) = -4 + 2 ∴ | + | = = = = 2 Comparing + , with = Rx + Ry ⇒ Rx = -4 and Ry = 2 Taking θ to be angle made by with X-axis, Answer: Magnitude and direction of + , is respectively 2 and and tan-1 with X – axis.
Solution & Step-by-Step Answer:
Substituting for wx in (i) using equation (ii), Using equation (ii), Answer: Required vector is –
Alternate method:
When two vectors are parallel, one vector is scalar multiple of another,
i.e., if and are parallel then, = n where, n is scalar.
Solution & Step-by-Step Answer:
Let angle between two vectors be θ. ⇒ Two vectors are parallel.
Alternate method:
= 2( + + ) = 2
Since is a scalar multiple of , the vectors are parallel.
3. Solve the following problems.
Solution & Step-by-Step Answer:
Using determinant for vectors in two dimensions, Answer: × gives
Solution & Step-by-Step Answer:
As dot product of two perpendicular vectors is zero. Taking dot product of and Combining two results, we can say that given three vectors , , and are mutually perpendicular to each other.
Solution & Step-by-Step Answer:
Answer: Required vector product is -7 + 5 +
Solution & Step-by-Step Answer:
As and are perpendicular to each other, θ = 90° Answer: Value of a is .
Solution & Step-by-Step Answer:
(i) x sin x Solution: [f1(x) × f2(x)] = f1(x) + f2(x) For f1(x) = x and f2(x) = sin x (x sin x) = x + sin x = x cos x + 1 × sin x = sin x + x cos x
(ii) x4+ cos x
Solution:
(iii)
Solution:
[Note: As derivative of (sin x) is cos x, negative sign that occurs in rule for differentiation for quotient of two functions gets retained in final answer]
Solution & Step-by-Step Answer:
Solution & Step-by-Step Answer:
(i) Solution:
(ii)
Solution:
11th Physics Digest Chapter 2 Mathematical MethodsIntext Questions and Answers
Can you recall? (Textbook Page No. 16)
Solution & Step-by-Step Answer:
Solution & Step-by-Step Answer:
Solution & Step-by-Step Answer:
No. | Scalars | Vectors |
i. | It has magnitude only | It has magnitude as well as direction. |
ii. | Scalars can be added or subtracted according to the rules of the algebra. | Vectors are added or subtracted by the geometrical (graphical) method or vector algebra. |
iii. | It has no specific representation. | It is represented by the symbol (→) arrow. |
iv. | The division of a scalar by another scalar is valid. | The division of a vector by another vector is not valid. |
| Example:
Length, mass, time, volume, etc. | Example:
Displacement, velocity, acceleration, force, etc. |
Internet my friend (Textbook page no. 28)
Answer:
[Students can use links given above as a reference and collect information about mathematical methods]