To determine the height at which a 6 kg weight is lifted to give it a gravitational potential energy of 70.56 joules, we can use the formula for gravitational potential energy:
[tex]\[ \text{Potential Energy} (PE) = \text{mass} (m) \times \text{gravitational acceleration} (g) \times \text{height} (h) \][/tex]
Given the values:
- Mass ([tex]\( m \)[/tex]) = 6 kg
- Gravitational acceleration ([tex]\( g \)[/tex]) = 9.8 m/s²
- Potential energy ([tex]\( PE \)[/tex]) = 70.56 J
We need to solve for the height ([tex]\( h \)[/tex]). Rearrange the formula to solve for [tex]\( h \)[/tex]:
[tex]\[ h = \frac{\text{Potential Energy}}{\text{mass} \times \text{gravitational acceleration}} \][/tex]
Substitute the given values into the formula:
[tex]\[ h = \frac{70.56 \, \text{J}}{6 \, \text{kg} \times 9.8 \, \text{m/s}^2} \][/tex]
Simplify:
[tex]\[ h = \frac{70.56}{58.8} \][/tex]
[tex]\[ h = 1.2 \, \text{m} \][/tex]
Therefore, the height at which the 6 kg weight is lifted to give it 70.56 joules of gravitational potential energy is:
[tex]\[ \boxed{1.2 \, \text{m}} \][/tex]
So the correct answer is:
B. 1.2 m
