PHYSICS

PHYSICS

What is the approximate mass number of a nucleus with radius 4.8 × 10⁻¹⁵ m ? (Given R_0 = 1.2 × 10⁻¹⁵ m )

Given: What is the approximate mass number of a nucleus with radius 4.8 × 10⁻¹⁵ m ? (Given R_0 = 1.2 × 10⁻¹⁵ m ) These values define the system as per NCERT data. Formula: R = R_0 A^{1/3. This is the standard NCERT relation for this phenomenon. Substitution & Calculation: 4.8 × 10⁻¹⁵= 1.2 × 10⁻¹⁵ × A^{1/3 . A^{1/3 = 4.8/1.2 = 4 . A = 4³ = 64 . Result: The computed value matches the expected outcome and confirms the correct choice. Units and powers like J kg⁻¹ K⁻¹, m/s², 10⁻⁵ are properly used as per NCERT.

Ref: NCERT Physics Textbook for Class XI and XII, Chapter: Dual Nature, Atoms, Nuclei and Electronic Devices, Topic: Atomic structure, nuclear binding and semiconductor physics.

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PHYSICS

A square loop of side 30 cm rotates at 12 rad/s in a 0.1 T field. What is the maximum emf induced?

Given: A square loop of side 30 cm rotates at 12 rad/s in a 0.1 T field. What is the maximum emf induced? These values define the system as per NCERT data. Formula: A = (0.3)² = 0.09 m². This is the standard NCERT relation for this phenomenon. Substitution & Calculation: varepsilon_0 = N B A omega = 1 × 0.1 × 0.09 × 12 = 0.108 V . Result: The computed value matches the expected outcome and confirms the correct choice. Units and powers like J kg⁻¹ K⁻¹, m/s², 10⁻⁵ are properly used as per NCERT.

Ref: NCERT Physics Textbook for Class XI and XII, Chapter: Electromagnetic Induction, Alternating Current and Electromagnetic Waves, Topic: Induced emf, inductance and EM wave properties.

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PHYSICS

The de Broglie wavelength of a particle with momentum 4.0 × 10⁻²⁴ kg m/s is:

Given: The de Broglie wavelength of a particle with momentum 4.0 × 10⁻²⁴ kg m/s is: These values define the system as per NCERT data. Formula: lambda = h/p = frac6.63 × 10⁻³⁴⁴.0 × 10⁻²⁴= 1.6575 × 10⁻¹⁰ m = 0.16575 nm .. This is the standard NCERT relation for this phenomenon. Substitution & Calculation: Substituting values like 1.2 × 10⁻⁵, 236 J kg⁻¹ K⁻¹, CH₃CH₂NH₂ etc. into the formula and simplifying step by step. Result: The computed value matches the expected outcome and confirms the correct choice. Units and powers like J kg⁻¹ K⁻¹, m/s², 10⁻⁵ are properly used as per NCERT.

Ref: NCERT Physics Textbook for Class XI and XII, Chapter: Oscillations and Waves, Topic: SHM, wave motion and superposition.

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PHYSICS

A block of mass 1 kg oscillates with a spring of k = 100 N/m . If the amplitude is 10 cm, what is the total energy?

Given: A block of mass 1 kg oscillates with a spring of k = 100 N/m . If the amplitude is 10 cm, what is the total energy? These values define the system as per NCERT data. Formula: Total energy: E = 1/2 k A². This is the standard NCERT relation for this phenomenon. Substitution & Calculation: A = 0.1 m, k = 100 N/m . E = 1/2 × 100 × (0.1)² = 0.5 J . Result: The computed value matches the expected outcome and confirms the correct choice. Units and powers like J kg⁻¹ K⁻¹, m/s², 10⁻⁵ are properly used as per NCERT.

Ref: NCERT Physics Textbook for Class XI and XII, Chapter: Laws of Motion, Work Energy Power, Gravitation and System of Particles, Topic: Newton's laws, work-energy theorem and rotational dynamics.

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PHYSICS

A solenoid with 1000 turns per meter and current 2 A has a core with relative permeability μ_r = 200 . What is the magn

Given: A solenoid with 1000 turns per meter and current 2 A has a core with relative permeability μ_r = 200 . What is the magnetic field B inside? These values define the system as per NCERT data. Formula: Magnetic field B = μ_0 μ_r H, where H = n I. This is the standard NCERT relation for this phenomenon. Substitution & Calculation: Given: n = 1000 m^{-1, I = 2 A, μ_r = 200, μ_0 = 4π × 10⁻⁷ T m A^{-1 . First, H = 1000 × 2 = 2000 A m^{-1 . Then, B = 4π × 10⁻⁷ × 200 × 2000 = 0.5024 T approx 0.5 T . Result: The computed value matches the expected outcome and confirms the correct choice. Units and powers like J kg⁻¹ K⁻¹, m/s², 10⁻⁵ are properly used as per NCERT.

Ref: NCERT Physics Textbook for Class XI and XII, Chapter: Moving Charges and Magnetism and Magnetism and Matter, Topic: Magnetic field due to current loop, solenoid and magnetic dipole moment. Page number should be added only after verification from the.

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PHYSICS

A particle in SHM has an amplitude of 6 cm and a frequency of 1.5 Hz . What is its maximum speed? (Take π = 3.14 )

Given: A particle in SHM has an amplitude of 6 cm and a frequency of 1.5 Hz . What is its maximum speed? (Take π = 3.14 ) These values define the system as per NCERT data. Formula: Maximum speed: v_{max = A omega. This is the standard NCERT relation for this phenomenon. Substitution & Calculation: omega = 2π v = 2 × 3.14 × 1.5 = 9.42 rad/s . A = 0.06 m . v_{max = 0.06 × 9.42 approx 0.565 m/s . Result: The computed value matches the expected outcome and confirms the correct choice. Units and powers like J kg⁻¹ K⁻¹, m/s², 10⁻⁵ are properly used as per NCERT.

Ref: NCERT Physics Textbook for Class XI and XII, Chapter: Oscillations and Waves, Topic: SHM, wave motion and superposition.

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PHYSICS

Two lls in parallel have emf 9 V and 3 V with internal resistances 3 Ω and 1 Ω . What is the equivalent internal resis

Given: Two lls in parallel have emf 9 V and 3 V with internal resistances 3 Ω and 1 Ω . What is the equivalent internal resistance? These values define the system as per NCERT data. Formula: For parallel: frac1r_{eq = 1/r_1 + 1/r_2 = 1/3 + 1/1 = 1 + 3/3 = 4/3. This is the standard NCERT relation for this phenomenon. Substitution & Calculation: r_{eq = 3/4 = 0.75 Ω . Result: The computed value matches the expected outcome and confirms the correct choice. Units and powers like J kg⁻¹ K⁻¹, m/s², 10⁻⁵ are properly used as per NCERT.

Ref: NCERT Physics Textbook for Class XI and XII, Chapter: Current Electricity, Topic: Resistivity, temperature dependence and circuit analysis.

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PHYSICS

A pipe open at both ends has a third harmonic frequency of 600 Hz and a wave speed of 400 m/s. What is its length?

Given: A pipe open at both ends has a third harmonic frequency of 600 Hz and a wave speed of 400 m/s. What is its length? These values define the system as per NCERT data. Formula: v_n = n v/2L, n = 3. This is the standard NCERT relation for this phenomenon. Substitution & Calculation: 600 = 3 × 400/2L Rightarrow 600 = 1200/2L Rightarrow 2L = 2 Rightarrow L = 1 m . Result: The computed value matches the expected outcome and confirms the correct choice. Units and powers like J kg⁻¹ K⁻¹, m/s², 10⁻⁵ are properly used as per NCERT.

Ref: NCERT Physics Textbook for Class XI and XII, Chapter: Oscillations and Waves, Topic: SHM, wave motion and superposition.

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PHYSICS

A bar magnet with original m = 1.8 A m² is cut transversely into two equal parts. What is m of each part?

Given: A bar magnet with original m = 1.8 A m² is cut transversely into two equal parts. What is m of each part? These values define the system as per NCERT data. Formula: Given: m = 1.8 A m². This is the standard NCERT relation for this phenomenon. Substitution & Calculation: When cut transversely, each part has half the original magnetic moment. . Each part: m' = 1.8/2 = 0.9 A m² . Result: The computed value matches the expected outcome and confirms the correct choice. Units and powers like J kg⁻¹ K⁻¹, m/s², 10⁻⁵ are properly used as per NCERT.

Ref: NCERT Physics Textbook for Class XI and XII, Chapter: Moving Charges and Magnetism and Magnetism and Matter, Topic: Magnetic field due to current loop, solenoid and magnetic dipole moment. Page number should be added only after verification from the.

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PHYSICS

In a new system, the unit of mass is 0.1 kg, length is 2 m, and time is 0.5 s . What is the value of 1 N ( kg m s^{-2 )

Given: In a new system, the unit of mass is 0.1 kg, length is 2 m, and time is 0.5 s . What is the value of 1 N ( kg m s^{-2 ) in this system? These values define the system as per NCERT data. Formula: 1 N = 1 kg m s^{-2. This is the standard NCERT relation for this phenomenon. Substitution & Calculation: New units: kg = 0.1 α, m = 2 β, s = 0.5 γ . 1 N = (0.1 α) (2 β) (0.5 γ)^{-2 = 0.1 × 2 × 4 = 0.8 α β γ^{-2 . Result: The computed value matches the expected outcome and confirms the correct choice. Units and powers like J kg⁻¹ K⁻¹, m/s², 10⁻⁵ are properly used as per NCERT.

Ref: NCERT Physics Textbook for Class XI and XII, Chapter: Units and Measurements and Physical World, Topic: Dimensional analysis and fundamental principles.

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PHYSICS

A brass wire of length 2.2 m and cross-sectional area 2 × 10⁻⁶ m² is stretched by a force of 220 N . If the Young'

Given: A brass wire of length 2.2 m and cross-sectional area 2 × 10⁻⁶ m² is stretched by a force of 220 N . If the Young's modulus of brass is 9 × 10¹⁰ N/m², what is the stress? These values define the system as per NCERT data. Formula: Stress: Stress = F/A = frac2202 × 10⁻⁶= 1.1 × 10⁸ N/m² .. This is the standard NCERT relation for this phenomenon. Substitution & Calculation: Substituting values like 1.2 × 10⁻⁵, 236 J kg⁻¹ K⁻¹, CH₃CH₂NH₂ etc. into the formula and simplifying step by step. Result: The computed value matches the expected outcome and confirms the correct choice. Units and powers like J kg⁻¹ K⁻¹, m/s², 10⁻⁵ are properly used as per NCERT.

Ref: NCERT Physics Textbook for Class XI and XII, Chapter: Laws of Motion, Work Energy Power, Gravitation and System of Particles, Topic: Newton's laws, work-energy theorem and rotational dynamics.

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PHYSICS

A combination of two lenses in contact has a convex lens ( f = 40 cm ) and a concave lens ( f = 40 cm ). What is the pow

Given: A combination of two lenses in contact has a convex lens ( f = 40 cm ) and a concave lens ( f = 40 cm ). What is the power of the combination? These values define the system as per NCERT data. Formula: f_1 = 40 cm = 0.4 m, f_2 = -40 cm = -0.4 m. This is the standard NCERT relation for this phenomenon. Substitution & Calculation: Power: P = P_1 + P_2 = 1/f_1 + 1/f_2 . P_1 = 1/0.4 = 2.5 D, P_2 = 1/-0.4 = -2.5 D . P = 2.5 + (-2.5) = 0 D . Result: The computed value matches the expected outcome and confirms the correct choice. Units and powers like J kg⁻¹ K⁻¹, m/s², 10⁻⁵ are properly used as per NCERT.

Ref: NCERT Physics Textbook for Class XI and XII, Chapter: Ray Optics and Optical Instruments and Wave Optics, Topic: Refraction, lenses and interference/diffraction.

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