Answer :
A body of mass 10 kg moving at a height of 2 m, with uniform speed of 2 m/s. its total energy is: b) 216 j.
To find the total energy of the body, we need to consider both its kinetic energy and its gravitational potential energy.
The total energy ([tex]\(E_{\text{total}}\)[/tex]) of the body is the sum of its kinetic energy ([tex]\(E_{\text{kinetic}}\)[/tex]) and its gravitational potential energy ([tex]\(E_{\text{potential}}\)[/tex]).
1. Kinetic energy [tex](\(E_{\text{kinetic}}\))[/tex] is given by:
[tex]\[ E_{\text{kinetic}} = \frac{1}{2} m v^2 \][/tex]
Where:
-m is the mass of the body
- v is the velocity of the body
Given that the mass (m) of the body is 10 kg and its velocity (v) is 2 m/s, let's calculate its kinetic energy:
[tex]\[ E_{\text{kinetic}} = \frac{1}{2} \times 10 \times (2)^2 \][/tex]
[tex]\[ E_{\text{kinetic}} = \frac{1}{2} \times 10 \times 4 \][/tex]
[tex]\[ E_{\text{kinetic}} = 20 \, \text{J} \][/tex]
2. Gravitational potential energy ([tex]\(E_{\text{potential}}\)[/tex]) is given by:
[tex]\[ E_{\text{potential}} = mgh \][/tex]
Where:
- m is the mass of the body
- g is the acceleration due to gravity
- h is the height
Given that the mass (m) of the body is 10 kg, the height (h) is 2 m, and the acceleration due to gravity (g) is approximately [tex]\(9.8 \, \text{m/s}^2\)[/tex], let's calculate its gravitational potential energy:
[tex]\[ E_{\text{potential}} = 10 \times 9.8 \times 2 \][/tex]
[tex]\[ E_{\text{potential}} = 196 \, \text{J} \][/tex]
Now, we can find the total energy [tex](\(E_{\text{total}}\))[/tex]:
[tex]\[ E_{\text{total}} = E_{\text{kinetic}} + E_{\text{potential}} \][/tex]
[tex]\[ E_{\text{total}} = 20 \, \text{J} + 196 \, \text{J} \][/tex]
[tex]\[ E_{\text{total}} = 216 \, \text{J} \][/tex]
So, the total energy of the body is 216.
Therefore, the correct option is (b) 216 J.
