If potential energy is given by U = r 2 a − r b . Then find out maximum force. (Given a = 2 , b = 4 )

F = − d r d u = − [ − r 3 2 a + r 2 b ] = r 3 2 a − r 2 b d r d F = r 4 − 6 a + r 3 2 b = 0 ⇒ r 6 a = 2 b ⇒ r = b 3 a = 4 6 = 2 3 ⇒ F m a x = ( 3/2 ) 3 2 × 2 − ( 3/2 ) 2 4 = 27 4 × 8 − 9 4 × 4 = 27 32 − 16 × 3 = − 27 16

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PhysicsW.E.P.MiscellaneousMedium2 minPYQ_2019

PhysicsMediumsingle choice

If potential energy is given by $U = \frac{a}{r ^{2}} - \frac{b}{r}$ . Then find out maximum force. (Given $a = 2$ , $b = 4)$

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$F = - \frac{d u}{d r} = - [- \frac{2 a}{r ^{3}} + \frac{b}{r ^{2}}] = \frac{2 a}{r ^{3}} - \frac{b}{r ^{2}} \frac{d F}{d r} = \frac{- 6 a}{r ^{4}} + \frac{2 b}{r ^{3}} = 0 \Rightarrow \frac{6 a}{r} = 2 b \Rightarrow r = \frac{3 a}{b} = \frac{6}{4} = \frac{3}{2} \Rightarrow F_{m a x} = \frac{2 \times 2}{( 3/2 ) ^{3}} - \frac{4}{( 3/2 ) ^{2}} = \frac{4 \times 8}{27} - \frac{4 \times 4}{9} = \frac{32 - 16 \times 3}{27} = - \frac{16}{27}$

Stream:AIIMSSubject:PhysicsTopic:W.E.P.Subtopic:Miscellaneous

⏱ 2mℹ️ Source: PYQ_2019

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