Energy — Important Questions

Four times the original value

Step 1: Original K.E. = ½ mv². Step 2: When speed is doubled, new speed = 2v. Step 3: New K.E. = ½ m(2v)² = ½ m × 4v² = 4 × (½ mv²) = 4 × original K.E. Key concept: Kinetic energy depends on the SQUARE of speed, so doubling the speed increases K.E. by 2² = 4 times. This is a very important result — the kinetic energy is proportional to v². Doubling speed does NOT double K.E.; it quadruples it.

400 J

Step 1: The increase in P.E. depends on the CHANGE in height, not the final height. Step 2: Change in height = h₂ − h₁ = 7 − 2 = 5 m. Step 3: Increase in P.E. = mg(h₂ − h₁) = 8 × 10 × 5 = 400 J. Why other options are wrong: 160 J uses only the initial height (8×10×2). 560 J uses only the final height (8×10×7). 720 J adds both heights (8×10×9). The key point is to use the DIFFERENCE in heights.

15 W

Step 1: Formula — Power P = Work done (W) / Time (t). Step 2: Substitute — W = 450 J, t = 30 s. Step 3: P = 450 / 30 = 15 W. Why other options are wrong: 150 W is obtained by dividing 450 by 3 (forgetting the zero in 30). 13500 W comes from multiplying W × t instead of dividing. 480 W comes from adding 450 + 30. Always DIVIDE work by time to get power.

Watt (W)

Step 1: Power = Work done / Time = Joules / Seconds = J/s. Step 2: The unit J/s has been given the special name 'Watt' (symbol W) in honour of scientist James Watt. Step 3: So the S.I. unit of power is Watt (W), where 1 W = 1 J/s. Why other options are wrong: Joule (J) is the unit of ENERGY or WORK, not power. Newton (N) is the unit of FORCE. Newton-metre (N·m) is the unit of work/energy (also called joule), not power.