Question

A particle of mass 10 kg is moving with velocity 10 (x)^1/2, here I is displacement. The work done by net force during the displacement of particle from x=4 to x=9

A) 1250 J B) 1000J C) 3500J D) 2500 J

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Answer 1

Answer:

Given that

m=10kg

v=10

x

m/s and

dx

dv

=

x

5

We know that

W=ma=m

dt

dv

=m

dt

dv

dx

dx

=mv

dx

dv

Hence

W=∫

x

1

x

2

mvdv=∫

4

9

10×10

x

x

5

dx=500[x]

4

9

=500(9−4)=2500J

Answer 2

Given:

Mass m = 10 kg.

Velocity v = 10√x

To find :

The work done by net force during the displacement of particle

from x=4 to x=9

Formula to be used:

Work done W = ma

Solution:

Step 1 of 2 :

The work done by net force during the displacement of particle

from x = 4 to x = 9 using the following formula,

W = ma

Here a = $\frac{dv}{dt}$

W = m $\frac{dv}{dt} \frac{dx}{dx}$

$\frac{dx}{dt} = v$

W = mv $\frac{dv}{dx}$

m = 10 kg

v = 10√x

$\frac{dv}{dx}$ = an$x^{n-1}$

a = 10 , x = $\frac{1}{2}$

$\frac{dv}{dx}$ = $10\frac{1}{2} (x^{\frac{1}{2}-1 } )$

$\frac{dv}{dx}$ = 5$x^{\frac{-1}{2} }$

$\frac{dv}{dx}$ = $5\frac{1}{\sqrt{x} }$

Step 2 of 2 :

$W=\int\limits^x_x {mv} \, dv$

$W=\int\limits^9_4 {10(10)\sqrt{x} \frac{5}{\sqrt{x} } } \, dx$

W = $500[x]^{9} _4$

W = 500( 9 - 4)

W= 500 (5)

W = 2500 J

Final answer:

A particle of mass 10 kg is moving with velocity 10 (x)^1/2, here I is displacement. The work done by net force during the displacement of particle from x = 4 to x = 9 is 2500 J .

Thus the correct option is (D) 2500 J