Explanation:
Escape velocity v_e = √(2GM/R), where M is planet mass, R its radius. Thus v_e depends on both M and R. It is independent of the escaping body's mass (as gravitational and inertial mass cancel). Memory tip: 'v_e ∝ √(M/R); larger M or smaller R ⇒ higher escape velocity'. This gravitation formula application is frequently tested in competitive exams. Always recall that escape velocity is a property of the planet, not the projectile. This problem assesses understanding of gravitational potential energy concepts.
Explanation:
The human ear retains the sensation of sound for about 0.1 seconds (persistence of hearing). To hear a distinct echo, the reflected sound must reach the ear after at least 0.1 s. Distance traveled by sound = Speed × Time = 344 m/s × 0.1 s = 34.4 m. Since this is the total distance (go and return), the minimum distance to the obstacle is 34.4 / 2 = 17.2 meters.
Explanation:
Resistance of a bulb is R = V^2 / P. The 60W bulb has a higher resistance than the 100W bulb. When connected in series, the exact same current (I) flows through both. The power consumed (which determines brightness) is given by P = I^2R. Since the 60W bulb has higher resistance (R), it consumes more power and glows brighter.
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