Question

the appropriate time taken by an engine of power 10 k W to lift a body of mass 100 kg through a height of 20 m​

Answer 1

Given :

Power of the engine = 10kW = 10000W

Mass of body = 100kg

Height = 20m

To Find :

Time taken by engine to lift the body.

Solution :

❖ Power is defined as the rate of work done per unit time.

• It is a scalar quantity having only magnitude.
• SI unit : W (watt)
• Dimension formula : [M¹L²T‾³]

Formula : $\underline{\boxed{\bf{\purple{Power=\dfrac{Work}{Time}}}}}$

We know that work done is measured as the product of force (mg) and displacement.

$\sf:\implies\:P=\dfrac{W}{t}=\dfrac{F\cdot d}{t}$

$\sf:\implies\:P=\dfrac{mg\cdot d}{t}$

By substituting the given values;

$\sf:\implies\:10000=\dfrac{(100)(10)(20)}{t}$

$\sf:\implies\:t=\dfrac{20000}{10000}$

$:\implies\:\underline{\boxed{\bf{\orange{t=2\:s}}}}$

Answer 2

Given :

Power of the engine = 10kW = 10000W

Mass of body = 100kg

Height = 20m

To Find :

Time taken by engine to lift the body.

Solution :

❖ Power is defined as the rate of work done per unit time.

It is a scalar quantity having only magnitude.

SI unit : W (watt)

Dimension formula : [M¹L²T‾³]

Formula :

Power= TimeWork

We know that work done is measured as the product of force (mg) and displacement.

⟹P= W t

= F⋅d t

:⟹P= mg⋅d t

By substituting the given values;

⟹10000= (100)(10)(20) t

⟹t=20000/10000

⟹ t=2s