Water falls from a 40m high dam at the rate of 9 × 10⁴ kg per hour. Fifty percentage of gravitational potential energy can be converted into electrical energy. Using this hydro electric energy, number of 100W lamps, that can be lit, is : (. Take g = 10ms⁻²) 

Concept:

Gravitational potential energy (GPE) can be converted into electrical energy. The formula for GPE is:

GPE = mgh

The electrical power generated can be found by converting the GPE to electrical energy and then dividing by time. Since only 50% of the GPE is converted, the formula becomes:

Electrical Power = 0.5 × (mgh / t)

Calculation:

We have,

⇒ m = 9 × 10⁴ kg per hour

⇒ h = 40 m

⇒ g = 10 m/s²

⇒ Time (t) = 3600 s (since 1 hour = 3600 seconds)

Calculate the gravitational potential energy:

⇒ GPE = mgh

⇒ GPE = 9 × 10⁴ kg × 10 m/s² × 40 m

⇒ GPE = 36 × 10⁶ J

Since only 50% of GPE is converted to electrical energy:

⇒ Electrical Energy = 0.5 × 36 × 10⁶ J

⇒ Electrical Energy = 18 × 10⁶ J

Now, calculate the electrical power generated:

⇒ Electrical Power = Electrical Energy / t

⇒ Electrical Power = 18 × 10⁶ J / 3600 s

⇒ Electrical Power = 5 × 10³ W

Each lamp is 100 W, so the number of 100 W lamps that can be lit:

⇒ Number of lamps = Total Power / Power per lamp

⇒ Number of lamps = 5 × 10³ W / 100 W

⇒ Number of lamps = 50

∴ The correct answer is option 2 (50).