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Physics

Mechanics

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Question

$straight A space uniform space solid space cylinder space of space mass space straight m space and space radius space straight R space is space placed space on space straight a space rough space horizontal space surface. space straight A space horizontal space constant space force space straight F space is space applied space at space the space top space point space straight P space of space the space cylinder space so space that space it space starts space pure space rolling. space The space acceleration space of space the space cylinder space is$

$F / 3 m$
$2 F / 3 m$
$4 F / 3 m$
$5 F / 3 m$

The correct answer is: $4 space straight F divided by 3 space straight m space space$

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$straight A space small space solid space sphere space of space mass space straight m space and space radius space straight r space starting space from space rest space from space the space rim space of space straight a space fixed space hemispherical space bowl space of space radius space straight R left parenthesis greater than greater than straight r right parenthesis space rolls space inside space it space without space sliding. space The space normal space reaction space exerted space by space the space sphere space on space the space hemisphere space when space it space reaches space the space bottom space of space hemisphere space is$

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$straight A space solid space sphere space of space mass space 10 space kg space is space placed space on space straight a space rough space surface space having space coefficient space of space friction space mu equals 0.1 space. space straight A space constant space force space straight F equals 7 space straight N space is space applied space along space line space passing space through space the space centre space of space the sphere space as space shown space in space the space figure. space The space value space of space frictional space force space left parenthesis in space straight N right parenthesis space on space the space sphere space is$

$straight A space solid space sphere space of space mass space 10 space kg space is space placed space on space straight a space rough space surface space having space coefficient space of space friction space mu equals 0.1 space. space straight A space constant space force space straight F equals 7 space straight N space is space applied space along space line space passing space through space the space centre space of space the sphere space as space shown space in space the space figure. space The space value space of space frictional space force space left parenthesis in space straight N right parenthesis space on space the space sphere space is$

PhysicsMechanics

$straight A space square space is space made space by space joining space four space rods space each space of space mass space straight M space and space length space straight L. space Its space moment space of space inertia space about space an space axis space PQ comma space in space its space plane space and space passing space through space one space of space its space corner space is$

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$straight A space spool space is space pulled space horizontally space on space rough space surface space by space two space equal space and space opposite space forces space as space shown space in space the space figure. space Which space of space the space following space statements space are space correct ?$

$straight A space spool space is space pulled space horizontally space on space rough space surface space by space two space equal space and space opposite space forces space as space shown space in space the space figure. space Which space of space the space following space statements space are space correct ?$

PhysicsMechanics

$straight A space solid space sphere space rolls space without space slipping space on space straight a space rough space horizontal space floor comma space moving space with space straight a space speed space straight v space space makes space an space elastic space collision space with space straight a space smooth space vertical space wall. space After space impact$

$straight A space solid space sphere space rolls space without space slipping space on space straight a space rough space horizontal space floor comma space moving space with space straight a space speed space straight v space space makes space an space elastic space collision space with space straight a space smooth space vertical space wall. space After space impact$

PhysicsMechanics

$straight A space particle space of space mass space space straight m equals 3 space kg space moves space along space straight a space straight space line space space 4 y minus 3 x equals 2 space space where space straight x space and space straight y space are space in space space metre comma space with space constant space velocity space space v equals 5 m s to the power of negative 1 end exponent space. space The space magnitude space of space angular space momentum space open parentheses kgm squared straight s to the power of negative 1 end exponent close parentheses space about space the space origin space is$

$straight A space particle space of space mass space space straight m equals 3 space kg space moves space along space straight a space straight space line space space 4 y minus 3 x equals 2 space space where space straight x space and space straight y space are space in space space metre comma space with space constant space velocity space space v equals 5 m s to the power of negative 1 end exponent space. space The space magnitude space of space angular space momentum space open parentheses kgm squared straight s to the power of negative 1 end exponent close parentheses space about space the space origin space is$

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$straight A space solid space homogeneous space sphere space is space moving space on space straight a space rough space horizontal space surface comma space partly space rolling space and space partly space sliding. space During space this space kind space of space motion space of space the space sphere.$

$straight A space solid space homogeneous space sphere space is space moving space on space straight a space rough space horizontal space surface comma space partly space rolling space and space partly space sliding. space During space this space kind space of space motion space of space the space sphere.$

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$For space the space same space total space mass comma space which space of space the space following space will space have space the space largest space moment space of space inertia space about space an space axis space passing space through space the space centre space of space mass space and space perpendicular space to space the space plane space of space the space body$

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PhysicsMechanics

$If space straight R space is space the space radius space of space gyration space of space straight a space body space of space mass space straight M space and space radius space straight r comma space then space the space ratio space of space its space rotational space to space translational space kinetic space energy space in space the space rolling space condition space is$

$If space straight R space is space the space radius space of space gyration space of space straight a space body space of space mass space straight M space and space radius space straight r comma space then space the space ratio space of space its space rotational space to space translational space kinetic space energy space in space the space rolling space condition space is$

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$straight A space circular space table space rotates space about space straight a space vertical space axis space with space straight a space constant space angular space speed space omega space space. space straight A space circular space straight A space circular space pan space rests space on space the space turn space table space left parenthesis with space the space centre space coinciding space with space centre space of space table right parenthesis space and space rotates space with space table. space The space bottom space of space the space pan space is space covered space with space straight a space uniform space small space thick space layer space of space ice space placed space at space centre space of space pan. space The space ice space starts space melting. space The space angular space speed space of space the space turn space table$

$straight A space circular space table space rotates space about space straight a space vertical space axis space with space straight a space constant space angular space speed space omega space space. space straight A space circular space straight A space circular space pan space rests space on space the space turn space table space left parenthesis with space the space centre space coinciding space with space centre space of space table right parenthesis space and space rotates space with space table. space The space bottom space of space the space pan space is space covered space with space straight a space uniform space small space thick space layer space of space ice space placed space at space centre space of space pan. space The space ice space starts space melting. space The space angular space speed space of space the space turn space table$

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$When space straight a space sphere space rolls space down space an space inclined space plane comma space then space identity space the space correct space statement space related space to space the space work space done space by space friction space force$

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PhysicsMechanics

$text Two identical rings end text straight A text and end text straight B text are acted upon by torques end text tau subscript A text and end text tau subscript B text respectively. A is rotating end text a b o u t space a n space a x i s space p a s sin g space t h r o u g h space t h e space c e n t r e space o f space m a s s space a n d space p e r p e n d i c u l a r space t o space t h e space p l a n e space o f space t h e space r i n g. space straight B text is rotating about a chord at a distance end text fraction numerator 1 over denominator square root of 2 end fraction text times the radius from the centre of the ring. If end text t h e space a n g u l a r space a c c e l e r a t i o n space o f space t h e space r i n g s space i s space t h e space s a m e comma space t h e n space$

$text Two identical rings end text straight A text and end text straight B text are acted upon by torques end text tau subscript A text and end text tau subscript B text respectively. A is rotating end text a b o u t space a n space a x i s space p a s sin g space t h r o u g h space t h e space c e n t r e space o f space m a s s space a n d space p e r p e n d i c u l a r space t o space t h e space p l a n e space o f space t h e space r i n g. space straight B text is rotating about a chord at a distance end text fraction numerator 1 over denominator square root of 2 end fraction text times the radius from the centre of the ring. If end text t h e space a n g u l a r space a c c e l e r a t i o n space o f space t h e space r i n g s space i s space t h e space s a m e comma space t h e n space$

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$text A box of mass end text 1 kg text is mounted with two cylinders each of mass end text 1 kg comma text moment of inertia end text 0.5 kgm squared a n d space r a d i u s space 1 m space a s space s h o w n space i n space f i g u r e comma space C y l i n d e r s space a r e space m o u n t e d space o n space t h e i r space c o n t r o l space a x i s space o f space r o t a t i o n space a n d space t h i s space s y s t e m space i s space p l a c e d space o n space a space r o u g h space h o r i z o n t a l space s u r f a c e comma space t h e space r e a r space c y l i n d e r space i s space c o n n e c t e d space t o space b a t t e r y space o p e r a t e d space m o t o r space w h i c h space p r o v i d e s space a space t o r q u e space o f space 100 n minus m space t o space t h i s space v space c y l i n d e r space v i a space a space b e l t space a s space s h o w n. space i f space s u f f i c i e n t space f r i c t i o n space i s space p r e s e n t space b e t w e e n space c y l i n d e r space a n d space h o r i z o n t a l space s u r f a c e space f o r space p u r e space r o l l i n g comma space f i n d space text acceleration of the vehicle in end text m over s squared. text (Neglect mass of motor, belt and other accessories of vehicle). end text$

$text A box of mass end text 1 kg text is mounted with two cylinders each of mass end text 1 kg comma text moment of inertia end text 0.5 kgm squared a n d space r a d i u s space 1 m space a s space s h o w n space i n space f i g u r e comma space C y l i n d e r s space a r e space m o u n t e d space o n space t h e i r space c o n t r o l space a x i s space o f space r o t a t i o n space a n d space t h i s space s y s t e m space i s space p l a c e d space o n space a space r o u g h space h o r i z o n t a l space s u r f a c e comma space t h e space r e a r space c y l i n d e r space i s space c o n n e c t e d space t o space b a t t e r y space o p e r a t e d space m o t o r space w h i c h space p r o v i d e s space a space t o r q u e space o f space 100 n minus m space t o space t h i s space v space c y l i n d e r space v i a space a space b e l t space a s space s h o w n. space i f space s u f f i c i e n t space f r i c t i o n space i s space p r e s e n t space b e t w e e n space c y l i n d e r space a n d space h o r i z o n t a l space s u r f a c e space f o r space p u r e space r o l l i n g comma space f i n d space text acceleration of the vehicle in end text m over s squared. text (Neglect mass of motor, belt and other accessories of vehicle). end text$

PhysicsMechanics

A thin wire of length L is bent into a circular wire of uniform linear density . When circular wire is in a vertical plane find the moment of inertia of loop about an axis BC, passing through centre of the loop and which makes an angle $theta$ with the tangent at the topmost point of the loop

A thin wire of length L is bent into a circular wire of uniform linear density . When circular wire is in a vertical plane find the moment of inertia of loop about an axis BC, passing through centre of the loop and which makes an angle $theta$ with the tangent at the topmost point of the loop

PhysicsMechanics

As shown in figure, the hinges A and B hold a uniform 400 N door in place. the upper hinge supports the entire weight of the door. Find the resultant force exerted on the door at the hinges. The width of the door is h/2, where h is the distance between the hinges.

As shown in figure, the hinges A and B hold a uniform 400 N door in place. the upper hinge supports the entire weight of the door. Find the resultant force exerted on the door at the hinges. The width of the door is h/2, where h is the distance between the hinges.

PhysicsMechanics

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