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physics

mechanics

Easy

Question

A solid cylinder of mass 10 kg is rolling perfectly on a plane of inclination 30⁰. The force of friction between the cylinder and the surface of the inclined plane is

49N
24.5N
49.3N
12.25N

The correct answer is: 49.3N

$f equals fraction numerator m g sin invisible function application theta over denominator 1 plus R squared over K squared end fraction text where end text R squared over K squared equals 2$

Related Questions to study

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A force F acts tangentially at the highest point of a solid cylinder of mass m kept on a rough horizontal plane. If the cylinder rolls without slipping, find the acceleration of the center of cylinder.

A force F acts tangentially at the highest point of a solid cylinder of mass m kept on a rough horizontal plane. If the cylinder rolls without slipping, find the acceleration of the center of cylinder.

PhysicsMechanics

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A solid sphere of mass M and radius R is placed in a rough horizontal surface. It is struck by a horizontal cue struck at a height h above the surface. The value of h so that the sphere performs pure rolling motion immediately after it has been hit is

A solid sphere of mass M and radius R is placed in a rough horizontal surface. It is struck by a horizontal cue struck at a height h above the surface. The value of h so that the sphere performs pure rolling motion immediately after it has been hit is

PhysicsMechanics

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$A space u n i f o r m space c i r c u l a r space r i n g space o f space r a d i u s space R space i s space f i r s t space r o t a t e d space a b o u t space i t s space h o r i z o n t a l space a x i s space w i t h space a n space a n g u l a r space text velocity end text omega subscript 0 text and then carefully placed on a rough horizontal surface as shown . The coefficient end text o f space f r i c t i o n space b e t w e e n space t h e space s u r f a c e space a n d space t h e space r i n g s space i s space space. space T i m e space a f t e r space w h i c h space i t s space a n g u l a r space s p e e d space i s space r e d u c e d space text to end text 0.5 omega subscript 0$

$A space u n i f o r m space c i r c u l a r space r i n g space o f space r a d i u s space R space i s space f i r s t space r o t a t e d space a b o u t space i t s space h o r i z o n t a l space a x i s space w i t h space a n space a n g u l a r space text velocity end text omega subscript 0 text and then carefully placed on a rough horizontal surface as shown . The coefficient end text o f space f r i c t i o n space b e t w e e n space t h e space s u r f a c e space a n d space t h e space r i n g s space i s space space. space T i m e space a f t e r space w h i c h space i t s space a n g u l a r space s p e e d space i s space r e d u c e d space text to end text 0.5 omega subscript 0$

PhysicsMechanics

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A disc is at rest at the top of a rough inclined plane. It rolls without slipping. At the bottom of inclined plane there is a vertical groove. the minimum height of incline required is

A disc is at rest at the top of a rough inclined plane. It rolls without slipping. At the bottom of inclined plane there is a vertical groove. the minimum height of incline required is

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Three particles are attached to a ring of mass m and radius R as shown in the figure. The centre of mass the ring has a speed and rolls without slipping on a horizontal surface. The kinetic energy of the system in the position shown in the figure

Three particles are attached to a ring of mass m and radius R as shown in the figure. The centre of mass the ring has a speed and rolls without slipping on a horizontal surface. The kinetic energy of the system in the position shown in the figure

PhysicsMechanics

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A horizontal force F is applied through the center of mass of a solid sphere of mass m and radius R which lies on a horizontal rough surface. If the sphere rolls without slipping, the acceleration of the center of mass of the sphere will be $open parentheses g equals 10 m divided by s squared close parentheses$

A horizontal force F is applied through the center of mass of a solid sphere of mass m and radius R which lies on a horizontal rough surface. If the sphere rolls without slipping, the acceleration of the center of mass of the sphere will be $open parentheses g equals 10 m divided by s squared close parentheses$

PhysicsMechanics

Mechanics

Physics

$straight A space uniform space rod space of space mass space straight M equals 2 kg space and space length space straight L space is space suspended space by space two space smooth space hinges space 1 space and space 2 space as space shown space in space figure. space straight A space force space straight F equals 4 straight N space is space applied space downward space at space straight a space distance space straight L divided by 4 space from space hinge space 2. space Due space to space the space application space of space force space straight F comma space hinge space 2 space breaks. space At space this space instant space comma space applied space force space straight F space is space also space removed. space The space rod space starts space to space rotate space downward space about space hinge space 1. space open parentheses g equals 10 m divided by s squared close parentheses$

$The space reaction space at space hinge space 1 comma space just space after space breaking space of space hinge space 2 comma space is space$

$straight A space uniform space rod space of space mass space straight M equals 2 kg space and space length space straight L space is space suspended space by space two space smooth space hinges space 1 space and space 2 space as space shown space in space figure. space straight A space force space straight F equals 4 straight N space is space applied space downward space at space straight a space distance space straight L divided by 4 space from space hinge space 2. space Due space to space the space application space of space force space straight F comma space hinge space 2 space breaks. space At space this space instant space comma space applied space force space straight F space is space also space removed. space The space rod space starts space to space rotate space downward space about space hinge space 1. space open parentheses g equals 10 m divided by s squared close parentheses$

$The space reaction space at space hinge space 1 comma space just space after space breaking space of space hinge space 2 comma space is space$

PhysicsMechanics

Mechanics

Physics

$straight A space uniform space rod space of space mass space straight M equals 2 kg space and space length space straight L space is space suspended space by space two space smooth space hinges space 1 space and space 2 space as space shown space in space figure. space straight A space force space straight F equals 4 straight N space is space applied space downward space at space straight a space distance space straight L divided by 4 space from space hinge space 2. space Due space to space the space application space of space force space straight F comma space hinge space 2 space breaks. space At space this space instant space comma space applied space force space straight F space is space also space removed. space The space rod space starts space to space rotate space downward space about space hinge space 1. space open parentheses g equals 10 m divided by s squared close parentheses$

$The space reaction space at space hinge space 1 comma space before space space hinge space 2 space breaks comma space is space$

$straight A space uniform space rod space of space mass space straight M equals 2 kg space and space length space straight L space is space suspended space by space two space smooth space hinges space 1 space and space 2 space as space shown space in space figure. space straight A space force space straight F equals 4 straight N space is space applied space downward space at space straight a space distance space straight L divided by 4 space from space hinge space 2. space Due space to space the space application space of space force space straight F comma space hinge space 2 space breaks. space At space this space instant space comma space applied space force space straight F space is space also space removed. space The space rod space starts space to space rotate space downward space about space hinge space 1. space open parentheses g equals 10 m divided by s squared close parentheses$

$The space reaction space at space hinge space 1 comma space before space space hinge space 2 space breaks comma space is space$

PhysicsMechanics

Mechanics

Physics

$straight A space body space of space mass space straight M space and space radius space straight R space is space as space shown space in space figure space. space The space body space can space be space straight a space ring space comma space straight a space disc comma space straight a space hollow space sphere space or space straight a space solid space I subscript x comma I subscript y. space space and space I subscript z space space are space the space moments space of space inertia space about space straight x comma straight y space and space straight z space axis space respectively. space Origin space coincides space with space centre space of space mass space of space the space body.$

Column I
Column II

i. $I subscript x equals I subscript y equals I subscript z$
a. possible for ring or disc

ii. $I subscript x equals I subscript y plus I subscript z$
b. possible for hollow sphere or solid sphere

iii. $I subscript y equals I subscript z plus I subscript x$
c. possible for all of the bodies mentioned

iv. $I subscript z equals I subscript x plus I subscript y$
d. not possible for any of the body mentioned

$straight A space body space of space mass space straight M space and space radius space straight R space is space as space shown space in space figure space. space The space body space can space be space straight a space ring space comma space straight a space disc comma space straight a space hollow space sphere space or space straight a space solid space I subscript x comma I subscript y. space space and space I subscript z space space are space the space moments space of space inertia space about space straight x comma straight y space and space straight z space axis space respectively. space Origin space coincides space with space centre space of space mass space of space the space body.$

Column I
Column II

i. $I subscript x equals I subscript y equals I subscript z$
a. possible for ring or disc

ii. $I subscript x equals I subscript y plus I subscript z$
b. possible for hollow sphere or solid sphere

iii. $I subscript y equals I subscript z plus I subscript x$
c. possible for all of the bodies mentioned

iv. $I subscript z equals I subscript x plus I subscript y$
d. not possible for any of the body mentioned

PhysicsMechanics

Mechanics

Physics

Two particles A and B of mass m each, are joined by a rigid massless rod of length l. A particle P of mass m, moving with speed u normal to AB, strikes A and stick to it. The centre of mass of the 'A + B + P' system after collision is C. If u = 4m/s, m = 3 kg, l = 3 m, then (All quantities in column are in SI units)

Two particles A and B of mass m each, are joined by a rigid massless rod of length l. A particle P of mass m, moving with speed u normal to AB, strikes A and stick to it. The centre of mass of the 'A + B + P' system after collision is C. If u = 4m/s, m = 3 kg, l = 3 m, then (All quantities in column are in SI units)

PhysicsMechanics

Mechanics

Physics

$In space Column space straight I comma space information space about space the space force left parenthesis straight s right parenthesis space acting space on space straight a space body space is space mentioned comma space while space in space Column space II space information space about space the space motion space of space straight a space body space is space given. space Match space the space entries space in space Column space II space with space the space entries space in space Column space straight I.$

Column I
Column II

i. A single force through centre of mass
a. Rotational motion

ii.Equal and opposite forces separated by non-zero distance
b. Translation motion

iii. Equal and opposite forces acting at the same point
c. No motion

iv. A single force not through centre of mass
d. Centre of mass performs translatory motion

$In space Column space straight I comma space information space about space the space force left parenthesis straight s right parenthesis space acting space on space straight a space body space is space mentioned comma space while space in space Column space II space information space about space the space motion space of space straight a space body space is space given. space Match space the space entries space in space Column space II space with space the space entries space in space Column space straight I.$

Column I
Column II

i. A single force through centre of mass
a. Rotational motion

ii.Equal and opposite forces separated by non-zero distance
b. Translation motion

iii. Equal and opposite forces acting at the same point
c. No motion

iv. A single force not through centre of mass
d. Centre of mass performs translatory motion

PhysicsMechanics

Mechanics

Physics

$From space straight a space uniform space disc space of space mass space straight M space and space radius space straight R comma space straight a space concentric space disc space of space radius space straight R divided by 2 space is space cut space out. space For space the space remaining space space annular space disc colon I subscript 1 space space space is space the space moment space of space inertia space about space axis space ‘ 1 ’ comma space space I subscript 2 space about space ‘ 2 ’ comma space space space space I subscript 3 italic space about space space ‘ 3 ’ comma space and space I subscript 4 space space space about space ‘ 4 ’. space Axes space ‘ 1 ’ space and space ‘ 2 ’ space are space perpendicular space to space the space disc space and space ‘ 3 ’ space and space ‘ 4 ’ space are space in space the space plane space of space the space disc. space Axes space ‘ 2 ’ comma ’ 3 ’ space and space ‘ 4 ’ space intersect space at space straight a space common space point. space Match space the space following space$

Column – I

Column – II

i. $I subscript 1$ is equal to
a. $21 over 32 M R squared$

ii. $I subscript 2$ is equal to
b. $I subscript 1 divided by 2$

iii. $I subscript 3 plus I subscript 4$ is equal to
c. $15 over 32 M R h 2$

iv. $I subscript 2 minus I subscript 3$ is equal to
d. none of these

$From space straight a space uniform space disc space of space mass space straight M space and space radius space straight R comma space straight a space concentric space disc space of space radius space straight R divided by 2 space is space cut space out. space For space the space remaining space space annular space disc colon I subscript 1 space space space is space the space moment space of space inertia space about space axis space ‘ 1 ’ comma space space I subscript 2 space about space ‘ 2 ’ comma space space space space I subscript 3 italic space about space space ‘ 3 ’ comma space and space I subscript 4 space space space about space ‘ 4 ’. space Axes space ‘ 1 ’ space and space ‘ 2 ’ space are space perpendicular space to space the space disc space and space ‘ 3 ’ space and space ‘ 4 ’ space are space in space the space plane space of space the space disc. space Axes space ‘ 2 ’ comma ’ 3 ’ space and space ‘ 4 ’ space intersect space at space straight a space common space point. space Match space the space following space$

Column – I

Column – II

i. $I subscript 1$ is equal to
a. $21 over 32 M R squared$

ii. $I subscript 2$ is equal to
b. $I subscript 1 divided by 2$

iii. $I subscript 3 plus I subscript 4$ is equal to
c. $15 over 32 M R h 2$

iv. $I subscript 2 minus I subscript 3$ is equal to
d. none of these

PhysicsMechanics

Mechanics

Physics

$End space straight A space space of space straight a space rod space AB space is space being space pulled space on space the space floor space with space straight a space constant space velocity space space v subscript 0 space as space shown. space Taking space the space length space of the space rod space as space l space comma space at space an space instant space when space the space rod space makes space an space angle space 37 to the power of 0 space space with space the space horizontal comma space calculate space space$

$The space angular space velocity space of space the space end space$

$End space straight A space space of space straight a space rod space AB space is space being space pulled space on space the space floor space with space straight a space constant space velocity space space v subscript 0 space as space shown. space Taking space the space length space of the space rod space as space l space comma space at space an space instant space when space the space rod space makes space an space angle space 37 to the power of 0 space space with space the space horizontal comma space calculate space space$

$The space angular space velocity space of space the space end space$

PhysicsMechanics

Mechanics

Physics

$End space straight A space space of space straight a space rod space AB space is space being space pulled space on space the space floor space with space straight a space constant space velocity space space v subscript 0 space as space shown. space Taking space the space length space of the space rod space as space space comma space at space an space instant space when space the space rod space makes space an space angle space 37 to the power of 0 space space with space the space horizontal comma space calculate$

$The space velocity space of space end space straight B$

$End space straight A space space of space straight a space rod space AB space is space being space pulled space on space the space floor space with space straight a space constant space velocity space space v subscript 0 space as space shown. space Taking space the space length space of the space rod space as space space comma space at space an space instant space when space the space rod space makes space an space angle space 37 to the power of 0 space space with space the space horizontal comma space calculate$

$The space velocity space of space end space straight B$

PhysicsMechanics

Mechanics

Physics

$straight A space uniform space rod space of space mass space straight M equals 2 kg space and space length space straight L space is space suspended space by space two space smooth space hinges space 1 space and space 2 space as space shown space in space figure. space straight A space force space straight F equals 4 straight N space is space applied space downward space at space straight a space distance space straight L divided by 4 space from space hinge space 2. space Due space to space the space application space of space force space straight F comma space hinge space 2 space breaks. space At space this space instant space comma space applied space force space straight F space is space also space removed. space The space rod space starts space to space rotate space downward space about space hinge space 1. space open italic left parenthesis g equals 10 m divided by s squared close parentheses$

$The space reaction space at space hinge space 1 comma space just space after space breaking space of space hinge space 2 comma space is space$

$straight A space uniform space rod space of space mass space straight M equals 2 kg space and space length space straight L space is space suspended space by space two space smooth space hinges space 1 space and space 2 space as space shown space in space figure. space straight A space force space straight F equals 4 straight N space is space applied space downward space at space straight a space distance space straight L divided by 4 space from space hinge space 2. space Due space to space the space application space of space force space straight F comma space hinge space 2 space breaks. space At space this space instant space comma space applied space force space straight F space is space also space removed. space The space rod space starts space to space rotate space downward space about space hinge space 1. space open italic left parenthesis g equals 10 m divided by s squared close parentheses$

$The space reaction space at space hinge space 1 comma space just space after space breaking space of space hinge space 2 comma space is space$

PhysicsMechanics

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