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Q123 (NDA-I/2023) Science & Technology › Basic Science (Physics, Chemistry, Biology) Official Key

The power required to lift a mass of 8.0 kg up a vertical distance of 4 m in 2 s is (taking acceleration due to gravity as 10 m/s2) :

Explanation

To calculate the power required to lift the mass, we use the fundamental physics relationship between work, energy, and time. Power (P) is defined as the rate at which work is done:

Power (P) = Work Done (W) / Time (t)

When an object is lifted vertically, the work done is equal to the Gravitational Potential Energy gained by the object, calculated using the formula:

  • Work (W) = m × g × h
  • Given: Mass (m) = 8.0 kg
  • Acceleration due to gravity (g) = 10 m/s²
  • Vertical distance (h) = 4 m
  • W = 8.0 × 10 × 4 = 320 Joules

Now, substituting the values into the power formula with the given time (t = 2 s):

Power (P) = 320 J / 2 s = 160 W

Therefore, the power required is 160 W, which aligns with Option B.

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