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A particle of mass m is moving in the x y-plane such that its velocity at a point (x, y) is given as \(\vec{v}=\alpha (y…

Q1

A particle of mass m is moving in the x y-plane such that its velocity at a point (x, y) is given as \(\vec{v}=\alpha (y\overset{^}{x}+2x\overset{^}{y})\), where \(\alpha\) is a non-zero constant. What is the force \(\vec{F}\) acting on the particle?

[JEE Advanced 2023]

a

\(\vec{F}=2m{\alpha }^{2}(x\overset{^}{x}+y\overset{^}{y})\)

b

\(\vec{F}=m{\alpha }^{2}(y\overset{^}{x}+2x\overset{^}{y})\)

c

\(\vec{F}=2m{\alpha }^{2}(y\overset{^}{x}+x\overset{^}{y})\)

d

\(\vec{F}=m{\alpha }^{2}(x\overset{^}{x}+2y\overset{^}{y})\)

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