A particle performs Simple Harmonic Motion (SHM). If its displacement from the mean position is half of its amplitude, the ratio of its kinetic energy to potential energy is: MCQ with Answer and Explanation
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Question #1
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A variable force F = (3x^2 + 2x) N acts on a particle. The work done by this force in moving the particle from x = 1 m to x = 2 m is:
Correct Answer: Option D
Explanation:
Work done by a variable force is the definite integral of F dx. W = Integral(3x^2 + 2x) dx from 1 to 2. W = [x^3 + x^2] evaluated from 1 to 2. Upper limit: (2^3 + 2^2) = 8 + 4 = 12. Lower limit: (1^3 + 1^2) = 1 + 1 = 2. Work = 12 - 2 = 10 Joules.
Work done by a variable force is the definite integral of F dx. W = Integral(3x^2 + 2x) dx from 1 to 2. W = [x^3 + x^2] evaluated from 1 to 2. Upper limit: (2^3 + 2^2) = 8 + 4 = 12. Lower limit: (1^3 + 1^2) = 1 + 1 = 2. Work = 12 - 2 = 10 Joules.
Question #2
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The magnetic field inside a long straight solenoid carrying current is:
Correct Answer: Option A
Explanation:
Inside a long solenoid, magnetic field is uniform (constant magnitude and direction), parallel to the axis, given by B = μ₀nI, where n is turns per unit length. Outside, field is nearly zero. This uniformity makes solenoids useful for creating controlled magnetic fields. Memory tip: 'Solenoid: uniform B inside like bar magnet'. This conceptual question tests knowledge of magnetic field configurations, crucial for electromagnetism in competitive exams. Always distinguish solenoid field (uniform inside) from straight wire field (circular, non-uniform).
Inside a long solenoid, magnetic field is uniform (constant magnitude and direction), parallel to the axis, given by B = μ₀nI, where n is turns per unit length. Outside, field is nearly zero. This uniformity makes solenoids useful for creating controlled magnetic fields. Memory tip: 'Solenoid: uniform B inside like bar magnet'. This conceptual question tests knowledge of magnetic field configurations, crucial for electromagnetism in competitive exams. Always distinguish solenoid field (uniform inside) from straight wire field (circular, non-uniform).
Question #3
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LED stands for
Correct Answer: Option B
Explanation:
LED (Light Emitting Diode) emits light when forward biased, due to recombination of electrons and holes. Efficient, long life. Used in displays, lighting. Laser is Light Amplification by Stimulated Emission of Radiation.
LED (Light Emitting Diode) emits light when forward biased, due to recombination of electrons and holes. Efficient, long life. Used in displays, lighting. Laser is Light Amplification by Stimulated Emission of Radiation.
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