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An electric dipole placed in a non-uniform electric field will experience
The correct answer is (c) Both force and torque. In a non-uniform electric field, an electric dipole experiences torque that aligns it with the field and force due to the field gradient. The force arises because the field strength differs at each dipole charge, causing a net translational motion. ToRead more
The correct answer is (c) Both force and torque.
In a non-uniform electric field, an electric dipole experiences torque that aligns it with the field and force due to the field gradient. The force arises because the field strength differs at each dipole charge, causing a net translational motion. Torque tends to rotate the dipole, aligning it with the field direction.
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A negatively charged object X is repelled by another charged object Y. However, an object Z is attracted to object Y. Which of the following is the most possibility for object Z?
The correct answer is (c) neutral or positively charged. Since X is negatively charged and repelled by Y, object Y must also be negatively charged. Object Z is attracted to Y, meaning Z could be either positively charged (opposite charges attract) or neutral (since a charged object can attract a neuRead more
The correct answer is (c) neutral or positively charged.
Since X is negatively charged and repelled by Y, object Y must also be negatively charged. Object Z is attracted to Y, meaning Z could be either positively charged (opposite charges attract) or neutral (since a charged object can attract a neutral object due to polarization).
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If a cos θ + b sinθ = 4 and a sin θ – b cos θ = 3, then a² + b² =
We are given the equations: a cosθ + b sinθ = 4 — (1) a sinθ - b cosθ = 3 — (2) We need to find the value of a² + b². Step 1: Square both equations Square both sides of equation (1): (a cosθ + b sinθ)² = 4² Expand the left-hand side: a² cos²θ + 2ab cosθ sinθ + b² sin²θ = 16 — (3) Square both sides oRead more
We are given the equations:
a cosθ + b sinθ = 4 — (1)
a sinθ – b cosθ = 3 — (2)
We need to find the value of a² + b².
Step 1: Square both equations
Square both sides of equation (1):
(a cosθ + b sinθ)² = 4²
Expand the left-hand side:
a² cos²θ + 2ab cosθ sinθ + b² sin²θ = 16 — (3)
Square both sides of equation (2):
(a sinθ – b cosθ)² = 3²
Expand the left-hand side:
a² sin²θ – 2ab sinθ cosθ + b² cos²θ = 9 — (4)
Step 2: Add equations (3) and (4)
Add the expanded forms of equations (3) and (4):
(a² cos²θ + 2ab cosθ sinθ + b² sin²θ) + (a² sin²θ – 2ab sinθ cosθ + b² cos²θ) = 16 + 9
Simplify the terms:
– The terms involving 2ab cosθ sinθ cancel out.
– Combine the remaining terms:
a² (cos²θ + sin²θ) + b² (sin²θ + cos²θ) = 25
Step 3: Use the Pythagorean identity
From the Pythagorean identity, we know:
cos²θ + sin²θ = 1.
Substitute this into the equation:
a² (1) + b² (1) = 25
Simplify:
a² + b² = 25.
The question is connected to Chapter 8, “Introduction to Trigonometry,” in the Class 10th NCERT Mathematics book. Respond based on your comprehension of the chapter.
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If sin θ – cos θ = 0, then the value of sin⁴ θ + cos⁴ θ is
Given: sinθ - cosθ = 0. 1. Solve for θ: sinθ = cosθ ⇒ tanθ = 1 ⇒ θ = 45°. 2. For θ = 45°: sinθ = cosθ = 1/√2. 3. Calculate sin⁴θ + cos⁴θ: sin⁴θ + cos⁴θ = (sin²θ)² + (cos²θ)² = (1/2)² + (1/2)² = 1/4 + 1/4 = 1/2. The question is based on Chapter 8 of the Class 10th NCERT Mathematics textbook, titled "Read more
Given: sinθ – cosθ = 0.
1. Solve for θ:
sinθ = cosθ ⇒ tanθ = 1 ⇒ θ = 45°.
2. For θ = 45°:
sinθ = cosθ = 1/√2.
3. Calculate sin⁴θ + cos⁴θ:
sin⁴θ + cos⁴θ = (sin²θ)² + (cos²θ)²
= (1/2)² + (1/2)²
= 1/4 + 1/4
= 1/2.
The question is based on Chapter 8 of the Class 10th NCERT Mathematics textbook, titled “Introduction to Trigonometry.” Provide your response in line with the concepts covered in this chapter.
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The value of (1 + cot θ – cosec θ) (1 + tan θ + sec θ) is
Given: (1 + cotθ - cosecθ)(1 + tanθ + secθ). 1. Rewrite in terms of sinθ and cosθ: (1 + cosθ/sinθ - 1/sinθ)(1 + sinθ/cosθ + 1/cosθ). 2. Simplify each factor: First factor: (sinθ + cosθ - 1)/sinθ. Second factor: (cosθ + sinθ + 1)/cosθ. 3. Multiply and simplify: Numerator: (sinθ + cosθ)² - 1 = 2sinθcoRead more
Given: (1 + cotθ – cosecθ)(1 + tanθ + secθ).
1. Rewrite in terms of sinθ and cosθ:
(1 + cosθ/sinθ – 1/sinθ)(1 + sinθ/cosθ + 1/cosθ).
2. Simplify each factor:
First factor: (sinθ + cosθ – 1)/sinθ.
Second factor: (cosθ + sinθ + 1)/cosθ.
3. Multiply and simplify:
Numerator: (sinθ + cosθ)² – 1 = 2sinθcosθ.
Denominator: sinθcosθ.
4. Result: 2sinθcosθ / sinθcosθ = 2.
This question related to Chapter 8 Mathematics Class 10th NCERT. From the Chapter 8 Introduction to Trigonometry. Give answer according to your understanding.
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