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A block of mass $$10$$ kg is moving along $$x$$-axis under the action of force $$F = 5x$$ N. The work done by the force in moving the block from $$x = 2$$ m to $$4$$ m will be _____ J.
Correct Answer: 30
Work done by a variable force: $$W = \int_{x_1}^{x_2} F \, dx$$
$$W = \int_2^4 5x \, dx = 5 \times \frac{x^2}{2}\bigg|_2^4 = \frac{5}{2}(16 - 4) = \frac{5}{2} \times 12 = 30 \text{ J}$$
The work done is $$\mathbf{30}$$ J.
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