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Physics

Mechanics

Easy

Question

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

125J
150J
250J
175J

The correct answer is: 250J

$M o m e n t space o f space i n e r t i a space o f space c o m p o s i t e space r o d space a b o u t space P I subscript P equals fraction numerator m ell squared over denominator 3 end fraction plus fraction numerator left parenthesis 2 straight m right parenthesis ell squared over denominator 12 end fraction plus 2 m open parentheses 3 over 2 ell close parentheses squared equals 5 m ell squared table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em rowspacing 3 pt end attributes row cell text Total kinetic energy end text k text total end text == 1 half I subscript P omega squared end cell row cell equals 1 half open parentheses 5 straight m ell squared close parentheses omega squared equals 5 over 2 m ell squared omega squared equals 250 straight J end cell end table$

Related Questions to study

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

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

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

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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

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PhysicsMechanics

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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

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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

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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

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PhysicsMechanics

parallel

A thin rod of length L and mass M is bent at the middle point O at an angle of 0 60 . The moment of inertia of the rod about an axis passing through O and perpendicular to the plane of the rod will be

A thin rod of length L and mass M is bent at the middle point O at an angle of 0 60 . The moment of inertia of the rod about an axis passing through O and perpendicular to the plane of the rod will be

PhysicsMechanics

Four identical solid spheres each of mass M and radius R are fixed at four corners of a light square frame of side length 4R such that centres of spheres coincide with corners of square. The moment of inertia of 4 spheres about an axis perpendicular to the plane of frame and passing through its centre is

Four identical solid spheres each of mass M and radius R are fixed at four corners of a light square frame of side length 4R such that centres of spheres coincide with corners of square. The moment of inertia of 4 spheres about an axis perpendicular to the plane of frame and passing through its centre is

PhysicsMechanics

A square plate of mass M and edge L is shown in figure. The moment of inertia of the plate about the axis in the plane of plate and passing through one of its vertex making an angle 15° with the horizontal is

A square plate of mass M and edge L is shown in figure. The moment of inertia of the plate about the axis in the plane of plate and passing through one of its vertex making an angle 15° with the horizontal is

PhysicsMechanics

parallel

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