For a rolling solid sphere, the acceleration \(a\) down an inclined plane can be calculated using the formula that accounts for both the translation and rotation of the sphere:
\[a = \frac{5}{7} g \sin(\theta)\]
where \(\theta\) is the angle of inclination and \(g\) is the acceleration due to gravity. Here, \(\theta = 30^\circ\) and \(g = 9.8 \, \text{m/s}^2\). Plugging in the values:
\[a = \frac{5}{7} \times 9.8 \times \sin(30^\circ) = \frac{5}{7} \times 9.8 \times 0.5 = 3.5 \, \text{m/s}^2\]
This result shows that the rolling motion includes not just the translational kinetic energy but also rotational kinetic energy, which slows the acceleration compared to sliding without rotation.
LIST I | LIST II | ||
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A. | Intrinsic semiconductor | I. Used as a rectifier circuit | |
B. | N-Type Semiconductor | II. Pure form of Semiconductor | |
C. | P-Type Semiconductor | III. Doping of pentavalent impurity in semiconductor | |
D. | P-N Junction diode | IV. Doping of trivalent impurity in semiconductor |
LIST I | LIST II | ||
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A. | Bipolar npn transistor operate in the cut-off mode. | I. The base-emitter is reverse biased and | |
B. | Bipolar npn transistor operate in the saturation mode. | II. Both the base-emitter and base | |
C. | Bipolar npn transistor operate in the inverse active mode. | III. The base-emitter is forward biased | |
D. | Bipolar npn transistor operate in the forward active mode. | IV. Both the base-emitter and bas |
LIST I | LIST II | ||
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A. | ∇ ⋅ E = ρ/ε₀ | I. Gauss's Law in magnetostatics | |
B. | ∇ ⋅ B = 0 | II. Faraday's Law of electromagnetic Induction | |
C. | ∇ × E = - ∂B/∂t | III. Gauss's Law in electrostatics | |
D. | ∇ × B = μ₀J + μ₀ε₀ ∂E/∂t | IV. Modified Ampere's Law |