Range R = u²sin(2θ)/g. sin(2θ) maximum (=1) when 2θ=90° ⇒ θ=45°. Standard result for level ground projection. Memory aid: 'Max range at 45°; max height at 90°'. Projectile motion fact frequently tested in competitive exams.
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Michael Faraday built the first electric generator (Faraday disk) in 1831, based on electromagnetic induction. Tesla contributed to AC motor and polyphase system. Edison DC systems. Watt steam engine.
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Atomic number Z = number of protons. Defines chemical element. Mass number = protons + neutrons. Isotopes same Z, different neutrons. Isobars same A, different Z.
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Weight on surface W = mg = 72 N. Acceleration due to gravity at height h is g' = g [R / (R+h)]². Here h = R/2. So, g' = g [R / (R + R/2)]² = g [1 / (3/2)]² = g (2/3)² = 4g/9. The new weight W' = mg' = m(4g/9) = (4/9)mg = (4/9) × 72 = 32 N.
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