Where

m = mass of the body,

m = mass of the body,

g is the acceleration due to gravity which is constant on earth.

Potential energy formula helps to calculate the mass, height or potential energy if any of the two quantities are given. It is expressed in Joules.

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Below are some problems based on potential energy.

### Solved Examples

**Question 1: **A ball of mass 2 Kg is kept on the hill of height 3Km. Calculate the potential energy possessed by it?

** Solution: **

Mass of the body (m) = 2kg,

Height (h) = 3 Km,

Potential Energy possessed by the body = m $\times$ g $\times$ h

Where g = 9.8 m/s^{2}

$\therefore$ Potential Energy = 2 kg $\times$ 9.8 m/s^{2} $\times$ 3 $\times$ 10^{3} m

= 6000 Kgm $\times$ 9.8 m/s^{2}

= 58800 Nm

= 58800 J.

**Question 2: **A boy is carrying a bucket of water of mass 5 Kg. If he does 500 J of work, to what height will he raise it?

** Solution: **

Mass of the water = m = 5Kg,

Potential energy P.E = 500 J,

Height h =?

Potential energy P.E = mgh

Height h = $\frac{P.E}{mg}$

= $\frac{500}{5 \times 9.8}$

= 10.2 m.

Mass of the body (m) = 2kg,

Height (h) = 3 Km,

Potential Energy possessed by the body = m $\times$ g $\times$ h

Where g = 9.8 m/s

$\therefore$ Potential Energy = 2 kg $\times$ 9.8 m/s

= 6000 Kgm $\times$ 9.8 m/s

= 58800 Nm

= 58800 J.

Mass of the water = m = 5Kg,

Potential energy P.E = 500 J,

Height h =?

Potential energy P.E = mgh

Height h = $\frac{P.E}{mg}$

= $\frac{500}{5 \times 9.8}$

= 10.2 m.

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