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) :
- (a)80 W
- (b)160 W
- (c)320 W
- (d)640 W
Correct — B, 160 W. Power is work done per unit time. The work to lift the mass is W = mgh = 8.0 x 10 x 4 = 320 J, done in 2 s, so P = 320/2 = 160 W.
- (a)80 W — This is mgh/t computed with a wrong figure (e.g. halving the work); the correct work is 320 J giving 160 W.
- (c)320 W — This is the WORK (320 J) mistaken for power, i.e. forgetting to divide by the time of 2 s.
- (d)640 W — This doubles the correct value; it would require twice the work or half the time.
Lifting a mass at steady speed against gravity does work equal to the gain in gravitational potential energy, W = mgh. Power is the rate of doing that work, P = W/t. With g taken as 10 m/s2, these give a clean numerical answer.
Compute the work first (mgh = 8 x 10 x 4 = 320 J), then divide by the 2-second time to get power (160 W). The common traps are quoting the work as power (320 W) or mis-scaling.
- Work against gravity: W = mgh.
- Power: P = W/t.
- Here W = 8 x 10 x 4 = 320 J; P = 320/2 = 160 W.
- 1 watt = 1 joule per second.
- Reporting the work (320 J) as the power.
- Forgetting to divide by the time.
Asked as the power to raise a mass through a height in a given time, using P = mgh/t.
No directly related past PYQ was found.
- practice — not a real PYQ
The power to lift 5 kg through 6 m in 3 s (g = 10 m/s2) is
- (a)100 W
- (b)300 W
- (c)50 W
- (d)150 W
Answer(a) 100 W (mgh/t = 300/3).
- practice — not a real PYQ
The SI unit of power is the
- (a)joule
- (b)watt
- (c)newton
- (d)pascal
Answer(b) watt (1 W = 1 J/s).