Question

Two persons do the same amount of work. The first
person does it in 10 s and the second, in 20 s. Find
the ratio of the power used by the first person to that
by the second person​

Answer 1

Answer:

The required ratio is 2 : 1

Explanation:

Given :

• Two persons do the same amount of work.
• The first  person does it in 10 s and the second, in 20 s.

To find :

the ratio of the power used by the first person to that  by the second person​

Solution :

Power :

• It is the rate of doing work.

• S.I unit of Power is Watt (W)

Let

• W be the amount of work.

• P₁ , P₂ be the power used by the first person and second person respectively.

• t₁ , t₂ be the time taken by the first person and second person to do the work respectively.

we know,

 $\underline{\boxed{\bf Power, P=\dfrac{Work \ done}{time \ taken}}}$

Power used by the first person,

P₁ = W/10

Power used by the second person,

P₂ = W/20

Ratio of the power used by the first person to that of second person :

 $\sf \dfrac{P_1}{P_2}=\dfrac{\dfrac{W}{10}}{\dfrac{W}{20}} \\\\\\ \sf \dfrac{P_1}{P_2}=\dfrac{20}{10} \\\\ \sf \dfrac{P_1}{P_2}=2$

∴ The required ratio is 2 : 1