Answer :
The machine, which dissipates power at a rate of 1 watt, does 5 joules of work in 5 seconds. This is equivalent to the gravitational potential energy needed to lift 500 grams of water to a height of 1 meter in 5 seconds, making the correct answer 500 grams (b). Therefore, the correct option is B.
To determine the mass of water that a machine can lift, we need to calculate the work done by the machine and then relate that to the work required to lift water. As given, the machine dissipates 60 watts every minute, which equates to 1 watt every second (since 60 watts/minute = 1 W/s). Now, we need to find out how much work the machine does in 5 seconds.
Work done = Power * Time, so the machine does 5 joules of work (1 watt * 5 seconds = 5 joules). This work is used to lift water against the force of gravity. The work required to lift the water is given by the formula for gravitational potential energy (GPE), which is GPE = mgh, where:
- m is the mass of the water,
- g is the acceleration due to gravity (10 m/s2),
- h is the height (1 m).
Setting the GPE equal to the work done (5 joules) gives us:
5 J = m imes 10 m/s2 imes 1 m
Solving for m, we get:
m = 5 J / (10 m/s2 imes 1 m)
m = 0.5 kg or 500 grams
Therefore, the mass of water the machine can lift to a height of 1 meter in 5 seconds is 500 grams (b).
