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A 2 kg ball is attached to a ceiling by a 1 m long string. The height of the room is 5 m. What is the gravitational potential energy associated with the ball relative to the floor?

a. 78
b. 98
c. 196
d. 245

Answer :

Final answer:

The gravitational potential energy of the ball relative to the floor is calculated using the formula GPE = mgh. The ball has 78.4 J of potential energy, which corresponds to option (b) 78 J. This is determined by using the mass of the ball, acceleration due to gravity, and the difference in height from the floor to the ball, accounting for the string length and room height.

Explanation:

The gravitational potential energy (GPE) of the ball relative to the floor can be calculated using the formula GPE = mgh, where 'm' is the mass of the object, 'g' is the acceleration due to gravity (9.8 m/s² on Earth), and 'h' is the height of the object from the reference point. In this scenario, the mass of the ball (m) is 2 kg, the acceleration due to gravity (g) is 9.8 m/s², and the height (h) from the floor is 4 m, since the ball hangs 1 m below the ceiling and the room is 5 m high. Using this information, the calculation is GPE = 2 kg × 9.8 m/s² × 4 m = 78.4 J. This value is closest to option (b) 78 J, which is the correct answer.

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