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Answer :
The machine can lift 500g of water to a height of 1m in 5 seconds by converting 50J of energy into work done against gravity, given that it dissipates 60W of power every minute and g=10 m/s². The correct answer is B.
The question pertains to energy conversion and power in the context of lifting a mass against gravity. Given that a machine dissipates 60W every minute, we can calculate the amount of energy used to lift water for 5 seconds. Since power is the rate at which work is done, it is given by power (P) = work (W) / time (t), which means work can be expressed as W = P * t. Thus, the work done in lifting water for 5 seconds is W = 60W * (5/60) s because the machine dissipates 60W every minute and we need to find the energy for only 5 seconds.
The work done is also described by lifting water against gravity, which is the change in gravitational potential energy (
potential energy): W = m * g * h, where m is mass, g is acceleration due to gravity, and h is the height. With the given g = 10 m/s² and h = 1m, we can set this equal to the previously calculated work to find the mass of water. Solving for m, we get m = W / (g*h).
Calculating these gives us the mass (m) of water that can be lifted as m = (60J * (5/60) s) / (10 m/s² * 1m), which simplifies to m = 0.5 kg. Therefore, the mass of water that can be lifted to a height of 1m in 5 seconds by the machine is 500g. The correct answer is B.
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