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Physics - Gravitation Question with Solution | TestHub

PhysicsGravitationField & ForceHard2 minPYQ_2019

PhysicsHardsingle choice

A straight rod of length $L$ extends from $x = a$ to $x = L + a .$ The gravitational force it exerts on a point mass 'm' at $x = 0,$ if the mass per unit length of the rod is $A + B x^{2},$ is given by:

Options:

Answer:

Solution:

$F = \int_{a}^{a + L} \frac{G m d M}{x^{2}} = Gm \int_{a}^{a + L} \frac{(A + B x^{2}) d x}{x^{2}}$

$= G m [\int_{a}^{a + L} \frac{A}{x^{2}} d x + \int_{a}^{a + L} B d x]$

$= G m [A {[\frac{- 1}{x}]}_{a}^{a + L} + B L]$

$= G m [A (\frac{1}{a} - \frac{1}{a + L}) + B L]$

Stream:JEESubject:PhysicsTopic:GravitationSubtopic:Field & Force

⏱ 2mℹ️ Source: PYQ_2019

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