(C) The work done is given by the line integral $W = \int \overrightarrow F \cdot d\overrightarrow r = \int (-K(y\hat i + x\hat j)) \cdot (dx\hat i +

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(C) The work done is given by the line integral $W = \int \overrightarrow F \cdot d\overrightarrow r = \int (-K(y\hat i + x\hat j)) \cdot (dx\hat i + dy\hat j) = -K \int (y\,dx + x\,dy) = -K \int d(xy)$.Path $1$: From $(0, 0)$ to $(a, 0)$. Here $y = 0$,so $dy = 0$. The work done $W_1 = -K \int_0^a (0) dx = 0$.Path $2$: From $(a, 0)$ to $(a, a)$. Here $x = a$,so $dx = 0$. The work done $W_2 = -K \int_0^a (a) dy = -K[ay]_0^a = -Ka^2$.Total work done $W = W_1 + W_2 = 0 + (-Ka^2) = -Ka^2$.

Class 11 Physics Work, Energy and Power Work Done by Variable Force and Force-Displacement Graph

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$A$ force $\overrightarrow F = - K(y\hat i + x\hat j)$ (where $K$ is a positive constant) acts on a particle moving in the $x-y$ plane. Starting from the origin,the particle is taken along the positive $x$-axis to the point $(a, 0)$ and then parallel to the $y$-axis to the point $(a, a)$. The total work done by the force $\overrightarrow F$ on the particle is

IIT 1998 All IIT

A
$ - 2Ka^2$
B
$2Ka^2$
C
$ - Ka^2$
D
$Ka^2$

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Work, Energy and Power

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Work Done by Variable Force and Force-Displacement Graph

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IIT 1998 Paper All IIT years →

$A$ body covers a distance of $2\,m$ under the influence of a force $F = 15 - 4x\,N$,where $x$ is the distance covered by the particle in meters. The work done by the force is ............ $J$.

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$A$ force acts on a particle moving along the $x$-axis,and its variation with position is shown in the figure. At which point will the particle be in a stable equilibrium position?

Medium

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$A$ particle moves along the $X$-axis from $x=0$ to $x=1 \, m$ under the influence of a force given by $F=3x^2+2x-10$. The work done in the process is ............. $J$.

Easy

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$A$ $10 \, kg$ mass moves along the $x-$axis. Its acceleration as a function of its position is shown in the figure. What is the total work done on the mass by the force as the mass moves from $x = 0$ to $x = 8 \, cm$?

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$A$ position-dependent force $F = (7 - 2x + 3x^2) \ N$ acts on a small object. The object is displaced from $x = 0$ to $x = 5 \ m$. What is the work done in Joules?

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$A$ body covers a distance of $2\,m$ under the influence of a force $F = 15 - 4x\,N$,where $x$ is the distance covered by the particle in meters. The work done by the force is ............ $J$.

$A$ force acts on a particle moving along the $x$-axis,and its variation with position is shown in the figure. At which point will the particle be in a stable equilibrium position?

$A$ particle moves along the $X$-axis from $x=0$ to $x=1 \, m$ under the influence of a force given by $F=3x^2+2x-10$. The work done in the process is ............. $J$.

$A$ $10 \, kg$ mass moves along the $x-$axis. Its acceleration as a function of its position is shown in the figure. What is the total work done on the mass by the force as the mass moves from $x = 0$ to $x = 8 \, cm$?

$A$ position-dependent force $F = (7 - 2x + 3x^2) \ N$ acts on a small object. The object is displaced from $x = 0$ to $x = 5 \ m$. What is the work done in Joules?

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