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The ratio of the power of X and Y is $4 : 3$ when X runs with a speed of $8 m / s$ against the frictional force of $10 N$ . Is it true that Y can run with the speed of $3 m / s$ against the frictional force of $20 N$ ?

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True

False

answer is A.

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Detailed Solution

The above statement is true.

Power (P) = \frac{work done}{time taken}

\Rightarrow

P = \frac{Fs}{t}

\Rightarrow

P = F \times v

[as

\frac{s}{t} = velocity (v)

]
Here

F =

force in newton

s =

displacement

t =

time

v =

velocity
Given,
In X case, frictional force

F_{X} = 10 N

The distance travelled by X

S_{X} = 8 m

In Y case, frictional force

F_{Y} = 20 N

Let the distance travelled by Y

= S_{Y}

The ratio of the power of X and Y is

4 : 3

\frac{P_{X}}{P_{Y}} = \frac{4}{3}

……..Eqn(1)

\Rightarrow

Power of X

P_{X} = (10 \times 8) / 1

= 80 W

\Rightarrow

Power of Y

= (20 \times S_{Y}) / 1

= 20 \times S_{Y}

Now from equation 1.

\frac{80}{20 S_{Y}} = \frac{4}{3}

S_{Y} = \frac{80 \times 3}{20 \times 4}

S_{Y} = 3 m

So the distance travelled by Y is

3 m

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