Question bank/JEE Main/Physics

A particle is moved under a force
$\overset{\rightarrow}{F} = x\overset{\hat{}}{j}N$(x in meter) from O to
A by two paths: path 1 is OBA andpath 2 is straight line OA. If w_1 and
w_2 are work done by the force $\overset{\rightarrow}{F}$ along the two
paths respectivelythe value of $\frac{w_{1}}{w_{2}}$is

A2B5C3D1

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work done in path 2
$W_{2} = \int\overset{\rightarrow}{F} \cdot (dx\overset{\hat{}}{i} + dy\overset{\hat{}}{j}) = \int x\overset{\hat{}}{j} \cdot (dx\overset{\hat{}}{i} + dy\overset{\hat{}}{j})$as
the line: y = x
$= \int_{0}^{1}{xdx} = \frac{1}{2}J$
work done in path 1
$w_{OB} = 0$ (force is zero)
$W_{1} = \int\overset{\rightarrow}{F} \cdot dx\overset{\hat{}}{i} + \int\overset{\rightarrow}{F} \cdot dy\overset{\hat{}}{j}$
$= 0 + \int_{y = 0}^{1}{(1\overset{\hat{}}{j}) \cdot dy\overset{\hat{}}{j} = 1J}$
$\frac{w_{1}}{w_{2}} = 2$

Source: Grass-G / P-16 Physics paper 25 Nov First.docx