CBSE Class 11-science Answered

1. A force is exerted on a particle in addition to the force of gravity, where is the velocity of the particle and is a constant vector in horizontal direction. With what minimum speed a particle must be projected so that it continues to move undeflected with a constant velocity.

Asked by Pavitra jain | 09 Sep, 2015, 06:27: PM

Expert Answer

Hi Pavitra Jain,

$begin mathsize 12px style Let space straight m space be space the space mass space of space the space particle. Let space straight v space be space the space velocity space with space whic space particle space is space projected space which space is space perpendicular space to space the space direction space of space stack straight A. with rightwards arrow on top Hence comma space theupward space force space on space particle space is comma straight F with rightwards arrow on top space equals space straight v with rightwards arrow on top space cross times space stack straight A space with rightwards arrow on top space equals space vA space sin 90 space equals space vA space space space space space left parenthesis straight i right parenthesis space The space gravitational space force space is space acting space on space straight a space particle space in space downward space direction comma space straight F space equals space mg space space space left parenthesis ii right parenthesis from space left parenthesis straight i right parenthesis space and space left parenthesis ii right parenthesis Let space straight m space be space the space mass space of space the space particle. Let space straight v space be space the space velocity space with space whic space particle space is space projected space which space is space perpendicular space to space the space direction space of space stack straight A. with rightwards arrow on top Hence comma space theupward space force space on space particle space is comma straight F with rightwards arrow on top space equals space straight v with rightwards arrow on top space cross times space stack straight A space with rightwards arrow on top space equals space vA space sin 90 space equals space vA space space space space space left parenthesis straight i right parenthesis space The space gravitational space force space is space acting space on space straight a space particle space in space downward space direction comma space straight F space equals space mg space space space left parenthesis ii right parenthesis from space left parenthesis straight i right parenthesis space and space left parenthesis ii right parenthesis space the space minimum space velocity space is comma vA space equals space mg rightwards double arrow space straight v space equals space mg over straight A end style$

Answered by | 09 Sep, 2015, 06:50: PM

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CBSE Class 11-science Answered

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