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Physics

Mechanics

Easy

Question

$space A space t h i n space minus w a l l e d space p i p e space r o l l s space a l o n g space t h e space f l o o r. space W h a t space i s space t h e space r a t i o space o f space i t s space t r a n s l a t i o n a l space k i n e t i c space e n e r g y space t o space i t s space r o t a t i o n a l space k i n e t i c space e n e r g y space a b o u t space t h e space c e n t r a l space a x i s space p a r a l l e l space t o space i t s space l e n g t h space ?$

1
3/2
2/3
4/3

The correct answer is: 1

$text The rotational kinetic energy is end text K equals 1 half I omega squared comma text where end text I equals m R squared text is its rotational inertia the centre of mas end text stack text The end text with _ below text ratio is end text K subscript text tram end text 1 end subscript over K subscript text tot end text end subscript equals fraction numerator 1 half m v subscript text com end text end subscript superscript 2 over denominator 1 half open parentheses m R squared close parentheses open parentheses v subscript text com end text end subscript divided by R close parentheses squared end fraction equals 1.00.$

Related Questions to study

$text A copper ball of mass end text straight m equals 1 kg text with a radius of end text straight r equals 10 cm text rotates with angular velocity end text omega equals 2 rad divided by straight s text about an axis passing through its centre. The work should be performed to increases the angular velocity of rotation of the end text text ball two fold is end text$

$text A copper ball of mass end text straight m equals 1 kg text with a radius of end text straight r equals 10 cm text rotates with angular velocity end text omega equals 2 rad divided by straight s text about an axis passing through its centre. The work should be performed to increases the angular velocity of rotation of the end text text ball two fold is end text$

PhysicsMechanics

A solid uniform disk of mass m and radius R is pivoted about a horizontal axis through its centre and a small body of mass m is attached to the rim of the disk. If the disk is released from rest with the small body, initially at the same level as the centre, the angular velocity when the small body reaches the lowest point of the disk is

A solid uniform disk of mass m and radius R is pivoted about a horizontal axis through its centre and a small body of mass m is attached to the rim of the disk. If the disk is released from rest with the small body, initially at the same level as the centre, the angular velocity when the small body reaches the lowest point of the disk is

PhysicsMechanics

$text A composite rod comprising two rods of mass end text straight m text and end text 2 straight m text and each of length end text l equals 1 straight m text as shown in the end text text figure. Assume end text omega equals 10 rad divided by straight s text and end text straight m equals 1 kg comma text the end text KE text of the rotating composite rod is end text$

$text A composite rod comprising two rods of mass end text straight m text and end text 2 straight m text and each of length end text l equals 1 straight m text as shown in the end text text figure. Assume end text omega equals 10 rad divided by straight s text and end text straight m equals 1 kg comma text the end text KE text of the rotating composite rod is end text$

PhysicsMechanics

parallel

$text A man stands on a rotating platform with his arms stretched holding a end text 5 kg text weight in each end text text hand. The angular speed of the platform is 1.2revs end text to the power of negative 1 end exponent text . The moment of inertia of the man together end text text with the platform may be taken to be constant and equal to end text 6 kgm squared text . If the man brings his arms end text c l o s e space t o space h i s space c h e s t space w i t h space t h e space d i s tan c e space n space e a c h space w e i g h t space f r o m space t h e space a x i s space c h a n g i n g space f r o m space 100 space c m space t o space 20 c m. space T h e space n e w space a n g u l a r space s p e e d space o f space t h e space p l a t f o r m space i s$

$text A man stands on a rotating platform with his arms stretched holding a end text 5 kg text weight in each end text text hand. The angular speed of the platform is 1.2revs end text to the power of negative 1 end exponent text . The moment of inertia of the man together end text text with the platform may be taken to be constant and equal to end text 6 kgm squared text . If the man brings his arms end text c l o s e space t o space h i s space c h e s t space w i t h space t h e space d i s tan c e space n space e a c h space w e i g h t space f r o m space t h e space a x i s space c h a n g i n g space f r o m space 100 space c m space t o space 20 c m. space T h e space n e w space a n g u l a r space s p e e d space o f space t h e space p l a t f o r m space i s$

PhysicsMechanics

$text Two discs of moments of inertia end text I subscript 1 text and end text I subscript 2 text about their respective axes, rotating with angular end text text frequencies, end text omega subscript 1 text and end text omega subscript 2 text respectively, are brought into contact face to face with their axes of end text text rotation coincident. The angular frequency of the composite disc will be A end text$

$text Two discs of moments of inertia end text I subscript 1 text and end text I subscript 2 text about their respective axes, rotating with angular end text text frequencies, end text omega subscript 1 text and end text omega subscript 2 text respectively, are brought into contact face to face with their axes of end text text rotation coincident. The angular frequency of the composite disc will be A end text$

PhysicsMechanics

$A space c h i l d space i s space s tan d i n g space w i t h space h i s space t w o space a r m s space o u t s t r e t c h e d space a t space t h e space c e n t r e space o f space a space t u r n t a b l e space t h a t space i s space r o t a t i n g space a b o u t space i t s space c e n t r a l space a x i s space w i t h space a n space a n g u l a r space s p e e d space omega subscript 0 space. space N o w comma space t h e space c h i l d space f o l d s space h i s space h a n d s space b a c k space s o space t h a t space m o m e n t space o f space i n e r t i a space b e c o m e s space 3 space t i m e s space t h e space i n i t i a l space v a l u e. space T h e space n e w space a n g u l a r space s p e e d space i s$

$A space c h i l d space i s space s tan d i n g space w i t h space h i s space t w o space a r m s space o u t s t r e t c h e d space a t space t h e space c e n t r e space o f space a space t u r n t a b l e space t h a t space i s space r o t a t i n g space a b o u t space i t s space c e n t r a l space a x i s space w i t h space a n space a n g u l a r space s p e e d space omega subscript 0 space. space N o w comma space t h e space c h i l d space f o l d s space h i s space h a n d s space b a c k space s o space t h a t space m o m e n t space o f space i n e r t i a space b e c o m e s space 3 space t i m e s space t h e space i n i t i a l space v a l u e. space T h e space n e w space a n g u l a r space s p e e d space i s$

PhysicsMechanics

parallel

$text A solid cylinder of mass end text 20 kg text and radius end text 20 cm text rotates about its axis with a angular speed end text 100 text rad end text s to the power of negative 1 end exponent. text The angular momentum of the cylinder about its axis is end text$

$text A solid cylinder of mass end text 20 kg text and radius end text 20 cm text rotates about its axis with a angular speed end text 100 text rad end text s to the power of negative 1 end exponent. text The angular momentum of the cylinder about its axis is end text$

PhysicsMechanics

$text A circular platform is mounted on a vertical frictionless axle. Its radius is end text r equals 2 m text and its moment end text text of inertia end text straight I equals 200 kgm squared text . It is initially at rest. A end text 70 kg text man stands on the edge of the platform and end text text begins to walk along the edge at speed end text v subscript 0 equals 1 ms to the power of negative 1 end exponent text relative to the ground. The angular velocity end text text of the platform is end text$

$text A circular platform is mounted on a vertical frictionless axle. Its radius is end text r equals 2 m text and its moment end text text of inertia end text straight I equals 200 kgm squared text . It is initially at rest. A end text 70 kg text man stands on the edge of the platform and end text text begins to walk along the edge at speed end text v subscript 0 equals 1 ms to the power of negative 1 end exponent text relative to the ground. The angular velocity end text text of the platform is end text$

PhysicsMechanics

$text A particle of mass end text 1 kg text is moving along the line end text straight y equals straight x plus 2 text (here end text straight x text and end text straight y text are in end text straight m text ) with speed end text 2 straight m divided by straight s text The magnitude of angular momentum of the particle about origin is: end text$

$text A particle of mass end text 1 kg text is moving along the line end text straight y equals straight x plus 2 text (here end text straight x text and end text straight y text are in end text straight m text ) with speed end text 2 straight m divided by straight s text The magnitude of angular momentum of the particle about origin is: end text$

PhysicsMechanics

parallel

$A space h o l l o w space s t r a i g h t space t u b e space o f space l e n g t h space l space a n d space m a s s space m space c a n space t u r n space f r e e l y space a b o u t space i t s space c e n t r e space left parenthesis f i x e d right parenthesis space o n space a space s m o o t h space h o r i z o n t a l space t a b l e. space A n o t h e r space s m o o t h space u n i f o r m space r o d space o f space s a m e space l e n g t h space a n d space m a s s space i s space f i t t e d space i n t o space t h e space t u b e space s o space t h a t space t h e i r space c e n t r e s space c o i n c i d e. space T h e space s y s t e m space i s space s e t space i n space m o t i o n space w i t h space a n space i n i t i a l space a n g u l a r space v e l o c i t y space omega subscript 0 space space. space T h e space a n g u l a r space v e l o c i t y space o f space t h e space r o d space a t space a n space i n s tan t space w h e n space t h e space r o d space s l i p s space o u t space o f space t h e space t u b e space i s colon$

$A space h o l l o w space s t r a i g h t space t u b e space o f space l e n g t h space l space a n d space m a s s space m space c a n space t u r n space f r e e l y space a b o u t space i t s space c e n t r e space left parenthesis f i x e d right parenthesis space o n space a space s m o o t h space h o r i z o n t a l space t a b l e. space A n o t h e r space s m o o t h space u n i f o r m space r o d space o f space s a m e space l e n g t h space a n d space m a s s space i s space f i t t e d space i n t o space t h e space t u b e space s o space t h a t space t h e i r space c e n t r e s space c o i n c i d e. space T h e space s y s t e m space i s space s e t space i n space m o t i o n space w i t h space a n space i n i t i a l space a n g u l a r space v e l o c i t y space omega subscript 0 space space. space T h e space a n g u l a r space v e l o c i t y space o f space t h e space r o d space a t space a n space i n s tan t space w h e n space t h e space r o d space s l i p s space o u t space o f space t h e space t u b e space i s colon$

PhysicsMechanics

The moment of inertia of a hollow sphere of mass M having internal and external radii R and 2R about an axis passing through its centre and perpendicular to its plane is

The moment of inertia of a hollow sphere of mass M having internal and external radii R and 2R about an axis passing through its centre and perpendicular to its plane is

PhysicsMechanics

Two circular loops A and B are made of the same wire and their radii are in the ratio 1:n.Their moments of inertia about the axis passing through the centre and perpendicular to their planes are in the ratio 1:m. The relation between m and n is

Two circular loops A and B are made of the same wire and their radii are in the ratio 1:n.Their moments of inertia about the axis passing through the centre and perpendicular to their planes are in the ratio 1:m. The relation between m and n is

PhysicsMechanics

parallel

Four thin metal rods, each of mass M and length L, are welded to form a square ABCD as shown in figure. The moment of inertia of the composite structure about a line which bisects rods AB and CD is

Four thin metal rods, each of mass M and length L, are welded to form a square ABCD as shown in figure. The moment of inertia of the composite structure about a line which bisects rods AB and CD is

PhysicsMechanics

Two rings of the same radius R and mass M are placed such that their centres coincide and their planes are perpendicular to each other. The moment of inertia of the system about an axis passing through the common centre and perpendicular to the plane of one of the rings is

Two rings of the same radius R and mass M are placed such that their centres coincide and their planes are perpendicular to each other. The moment of inertia of the system about an axis passing through the common centre and perpendicular to the plane of one of the rings is

PhysicsMechanics

A uniform circular disc of radius 'R' lies in the X-Y plane with the centre coinciding with the origin. The moment of inertia about an axis passing through a point on the X-axis at a distance x = 2R and perpendicular to the X-Y plane is equal to its moment of inertia about an axis passing through a point on the Y-axis at a distance y = d and parallel to the X-axis in the X-Y plane. The value of 'd' is

A uniform circular disc of radius 'R' lies in the X-Y plane with the centre coinciding with the origin. The moment of inertia about an axis passing through a point on the X-axis at a distance x = 2R and perpendicular to the X-Y plane is equal to its moment of inertia about an axis passing through a point on the Y-axis at a distance y = d and parallel to the X-axis in the X-Y plane. The value of 'd' is

PhysicsMechanics

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