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Work Power and Energy question

2023 · 15 Apr · Shift 1 · Q68

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Work Power and Energy
2023 · 15 Apr · Shift 1 · Q68

Work Power and Energy question

2023 · 15 Apr · Shift 1 · Q68

JEE MainPhysicsWork Power and EnergyNumerical+4 / −1

A block of mass

10 \mathrm{~kg}

is moving along

\mathrm{x}

-axis under the action of force

F=5 x~ N

. The work done by the force in moving the block from

x=2 m

to

4 m

will be

\underline{\hspace{2cm}}

J.

Numerical answer

View written solutionFree

Correct answer: 30

The force depends on position:

$F(x)=5x \text{ N}$

Work done by a variable force from $x=2$ m to $x=4$ m is

$W=\int_{2}^{4} F(x)\,dx$

Substitute $F(x)=5x$ :

$W=\int_{2}^{4} 5x\,dx$

Integrate:

$\int 5x\,dx=\frac{5x^2}{2}$

So,

$W=\left[\frac{5x^2}{2}\right]_{2}^{4}$

Apply limits:

$W=\frac{5}{2}(4^2-2^2)=\frac{5}{2}(16-4)=\frac{5}{2}\cdot 12=30$

Therefore, the work done is

$\boxed{30\text{ J}}$

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