Physics - Gravitation Question with Solution | TestHub

PhysicsGravitationField & ForceEasy2 minPYQ_2020

PhysicsEasysingle choice

Two identical blocks of mass $m$ are suspended from a beam balance whose scale pans differ in vertical height by $h (≪ R)$ , If $R$ and $ρ$ are the radius and density of the earth, then the error in weighing is

Options:

Answer:

Solution:

As with height $g$ varies as

and in accord with the figure $h_{1} > h_{2}$ so $W_{1}$ will be lesser than $W_{2}$ and

$W_{2} - W_{1} = {mg}_{2} - {mg}_{1} = 2 mg [\frac{h_{1}}{R} - \frac{h_{2}}{R}]$

or $W_{2} - W_{1} = 2 m \frac{GM}{R^{2}} \frac{h}{R}$

$[as g = \frac{GM}{R^{2}} and (h_{1} - h_{2}) = h]$

or $W_{2} - W_{1} = \frac{2 mhG}{R^{3}} (\frac{4}{3} {πR}^{3} ρ)$

$= \frac{8}{3} πρGmh [as M = \frac{4}{3} {πR}^{3} ρ]$

Subject:PhysicsTopic:GravitationSubtopic:Field & Force

⏱ 2mℹ️ Source: PYQ_2020

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