A block is constrained to move along x-axis under a force F- 4-x2 x- 0 - Here- F is in newton and x in metre- Find the work done by this force when the block is displaced from x-4 m to x-2 m-

The correct option is A 1 JWork done in moving an object from x_1 to x_2 =∫_x_1^x_2Fdx =∫_x_1^x_24x^2dx =4(1x_1 1x_2) =4(14 12) ...

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Byju's Answer

Standard XII

Physics

Work Done When Force Is Varying

A block is co...

Question

A block is constrained to move along x-axis under a force $F = \frac{4}{x^{2}} (x \neq 0) .$ Here, F is in newton and x in metre. Find the work done by this force when the block is displaced from x=4 m to x=2 m.

-1 J

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Solution

The correct option is A -1 J
Work done in moving an object from $x_{1}$ to $x_{2}$
$= \int_{x_{1}}^{x_{2}} F d x$
$= \int_{x_{1}}^{x_{2}} \frac{4}{x^{2}} d x$
$= 4 (\frac{1}{x_{1}} - \frac{1}{x_{2}})$
$= 4 (\frac{1}{4} - \frac{1}{2})$
$= - 1 J$

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A block is constrained to move along x-axis under a force F=4x2(x≠0). Here, F is in newton and x in metre. Find the work done by this force when the block is displaced from x=4 m to x=2 m.

The correct option is A -1 JWork done in moving an object from x1 to x2=∫x2x1Fdx=∫x2x14x2dx=4(1x1−1x2)=4(14−12)=−1J

A block is constrained to move along x-axis under a force $F = \frac{4}{x^{2}} (x \neq 0) .$ Here, F is in newton and x in metre. Find the work done by this force when the block is displaced from x=4 m to x=2 m.

The correct option is A -1 J
Work done in moving an object from $x_{1}$ to $x_{2}$
$= \int_{x_{1}}^{x_{2}} F d x$
$= \int_{x_{1}}^{x_{2}} \frac{4}{x^{2}} d x$
$= 4 (\frac{1}{x_{1}} - \frac{1}{x_{2}})$
$= 4 (\frac{1}{4} - \frac{1}{2})$
$= - 1 J$