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Physics

Mechanics

Easy

Question

Four masses 'm' each are orbiting in a circle of radius 'r' in the same direction under gravitational force. Velocity of each particle is

$\sqrt{\frac{G m}{r} \frac{(1 + 2 \sqrt{2})}{2}}$
$\sqrt{\frac{G m}{r}}$
$\sqrt{\frac{G m}{r} (1 + 2 \sqrt{2})}$
$\sqrt{\frac{G m}{2 r} (\frac{1 + 2 \sqrt{2}}{2})}$

The correct answer is: $square root of fraction numerator G m over denominator 2 r end fraction open parentheses fraction numerator 1 plus 2 square root of 2 over denominator 2 end fraction close parentheses end root$

$fraction numerator G m squared over denominator left parenthesis 2 r right parenthesis squared end fraction plus fraction numerator 2 G m squared over denominator left parenthesis square root of 2 r end root right parenthesis squared end fraction cos invisible function application 45 to the power of ring operator equals fraction numerator m v squared over denominator r end fraction$

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$text The gravitational field in a region is end text 10 straight N divided by kg left parenthesis straight i with not stretchy hat on top minus straight j with not stretchy hat on top right parenthesis. text Then the work done by end text g r a v i t a t i o n a l space f o r c e space t o space s h i f t space s l o w l y space a space p a r t i c l e space o f space m a s s space 1 k g space f r o m space p o i n t space left parenthesis 1 m comma space 1 m right parenthesis space t o space a space p o i n t space left parenthesis 2 m comma space – 2 m right parenthesis space i s space minus space space$

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