(A) The work done $W$ by a variable force $\vec F$ is given by the line integral: $W = \int \vec F \cdot d\vec r$.Given $\vec F = (2x\hat i + y\hat j)

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(A) The work done $W$ by a variable force $\vec F$ is given by the line integral: $W = \int \vec F \cdot d\vec r$.Given $\vec F = (2x\hat i + y\hat j)$ and $d\vec r = (dx\hat i + dy\hat j)$.$W = \int_{(0,0)}^{(1,2)} (2x\hat i + y\hat j) \cdot (dx\hat i + dy\hat j) = \int_{(0,0)}^{(1,2)} (2x\,dx + y\,dy)$.Integrating the terms separately:$W = \int_{0}^{1} 2x\,dx + \int_{0}^{2} y\,dy$.$W = [x^2]_{0}^{1} + [\frac{y^2}{2}]_{0}^{2}$.$W = (1^2 - 0^2) + (\frac{2^2}{2} - \frac{0^2}{2})$.$W = 1 + \frac{4}{2} = 1 + 2 = 3\,units$.

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

Medium

$A$ body of mass $200\,g$ is moving along the $XY$ plane. The work performed by the force given by $\vec F = (2x\hat i + y\hat j)$ acting on it when the body is displaced from $(0, 0)$ to $(1, 2)$ will be equal to ............... $unit$.

A
$3$
B
$6$
C
$5$
D
$1.5$

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Work, Energy and Power

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Work Done by Variable Force and Force-Displacement Graph

Consider a force $\overrightarrow{F}=-x \hat{i}+y \hat{j}$. The work done by this force in moving a particle from point $A(1,0)$ to $B(0,1)$ along the line segment is (all quantities are in $SI$ units).

MediumJEE MAIN 2020

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$A$ force $F = 20 + 10y$ acts on a particle in the $y$ direction,where $F$ is in newton $(N)$ and $y$ is in meter $(m)$. The work done by this force to move the particle from $y = 0$ to $y = 1 \; m$ is ...... $J$.

MediumNEET 2019

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Force acting on a body of mass $1 \ kg$ is related to its position $x$ as $F = x^3 - 3x \ N$. It is at rest at $x = 1$. Its velocity at $x = 3$ can be ......... $m/s$.

Difficult

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$A$ force $F$ acting on an object varies with distance $x$ as shown in the graph. The force is in $N$ and $x$ is in $m$. The work done by the force in moving the object from $x = 0$ to $x = 6$ is ............. $J$.

Easy

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The adjacent figure shows the force-displacement graph of a moving body. What is the work done by this force in displacing the body from $x = 0$ to $x = 35\,m$ (in $,J$)?

Difficult

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$A$ body of mass $200\,g$ is moving along the $XY$ plane. The work performed by the force given by $\vec F = (2x\hat i + y\hat j)$ acting on it when the body is displaced from $(0, 0)$ to $(1, 2)$ will be equal to ............... $unit$.

Similar Questions

Consider a force $\overrightarrow{F}=-x \hat{i}+y \hat{j}$. The work done by this force in moving a particle from point $A(1,0)$ to $B(0,1)$ along the line segment is (all quantities are in $SI$ units).

$A$ force $F = 20 + 10y$ acts on a particle in the $y$ direction,where $F$ is in newton $(N)$ and $y$ is in meter $(m)$. The work done by this force to move the particle from $y = 0$ to $y = 1 \; m$ is ...... $J$.

Force acting on a body of mass $1 \ kg$ is related to its position $x$ as $F = x^3 - 3x \ N$. It is at rest at $x = 1$. Its velocity at $x = 3$ can be ......... $m/s$.

$A$ force $F$ acting on an object varies with distance $x$ as shown in the graph. The force is in $N$ and $x$ is in $m$. The work done by the force in moving the object from $x = 0$ to $x = 6$ is ............. $J$.

The adjacent figure shows the force-displacement graph of a moving body. What is the work done by this force in displacing the body from $x = 0$ to $x = 35\,m$ (in $,J$)?

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