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Physics

Mechanics

Easy

Question

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

$\frac{R^{2}}{R^{2} + r^{2}}$
$\frac{R^{2}}{r^{2}}$
$\frac{r^{2}}{R^{2}}$
$1$

The correct answer is: $R squared over r squared$

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

PhysicsMechanics

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

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

PhysicsMechanics

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

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

PhysicsMechanics

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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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$A space r i n g space o f space m a s s space M space a n d space r a d i u s space R space l i e s space i n space x minus y space p l a n e space w i t h space i t s space c e n t r e space a t space o r i g i n space a s space s h o w n. space T h e space m a s s space d i s t r i b u t i o n space o f space r i n g s space i s space n o n minus u n i f o r m space s u c h space t h a t space a t space a n y space p o i n t space P space o n space t h e space r i n g comma space t h e space m a s s space p e r space u n i t space text length is given by end text lambda equals lambda subscript 0 cos squared invisible function application theta text (where end text lambda subscript 0 text is a positive constant). Then the moment of inertia of end text t h e space r i n g space a b o u t space z minus space a x i s space i s$

$A space r i n g space o f space m a s s space M space a n d space r a d i u s space R space l i e s space i n space x minus y space p l a n e space w i t h space i t s space c e n t r e space a t space o r i g i n space a s space s h o w n. space T h e space m a s s space d i s t r i b u t i o n space o f space r i n g s space i s space n o n minus u n i f o r m space s u c h space t h a t space a t space a n y space p o i n t space P space o n space t h e space r i n g comma space t h e space m a s s space p e r space u n i t space text length is given by end text lambda equals lambda subscript 0 cos squared invisible function application theta text (where end text lambda subscript 0 text is a positive constant). Then the moment of inertia of end text t h e space r i n g space a b o u t space z minus space a x i s space i s$

PhysicsMechanics

A ring of mass m and radius R is rolling down on a rough inclined plane of angle with horizontal. Plot the angular momentum of the ring about the point of contact of ring and the plane as a function of time.

A ring of mass m and radius R is rolling down on a rough inclined plane of angle with horizontal. Plot the angular momentum of the ring about the point of contact of ring and the plane as a function of time.

PhysicsMechanics

A spool of mass M and internal and external radii R and 2R hanging from a rope touches a curved surface, as shown. A block of mass m placed on a rough surface inclined at an angle a with horizontal is attached with other end of the rope. The pulley is massless and system is in equilibrium. Find the coefficient of friction

A spool of mass M and internal and external radii R and 2R hanging from a rope touches a curved surface, as shown. A block of mass m placed on a rough surface inclined at an angle a with horizontal is attached with other end of the rope. The pulley is massless and system is in equilibrium. Find the coefficient of friction

PhysicsMechanics

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Two point masses A of mass M and B of mass 4M are fixed at the ends of a rod of length l and of negligible mass. The rod is set rotation about an axis perpendicular to its length with a uniform angular speed. The work required for rotating the rod will be minimum when the distance of axis of rotation from the mass A is at

Two point masses A of mass M and B of mass 4M are fixed at the ends of a rod of length l and of negligible mass. The rod is set rotation about an axis perpendicular to its length with a uniform angular speed. The work required for rotating the rod will be minimum when the distance of axis of rotation from the mass A is at

PhysicsMechanics

Let I be the moment of inertia of a uniform square plate about an axis AB that passes through its centre and is parallel to two of its sides. CD is a line in the plane of the plate that passes through the centre of the plate and makes an angle with AB. Then the moment of inertia of the plate about the axis CD is equal to :

Let I be the moment of inertia of a uniform square plate about an axis AB that passes through its centre and is parallel to two of its sides. CD is a line in the plane of the plate that passes through the centre of the plate and makes an angle with AB. Then the moment of inertia of the plate about the axis CD is equal to :

PhysicsMechanics

Two light vertical springs with equal natural lengths and spring constants K₁ and K₂and are separated by a distance l. Their upper ends are fixed to the ceiling and their lower ends to the ends A and B of a light horizontal rod AB. A vertical downwards force F is applied at point C on the rod. AB will remain horizontal in equilibrium if the distance AC is :

Two light vertical springs with equal natural lengths and spring constants K₁ and K₂and are separated by a distance l. Their upper ends are fixed to the ceiling and their lower ends to the ends A and B of a light horizontal rod AB. A vertical downwards force F is applied at point C on the rod. AB will remain horizontal in equilibrium if the distance AC is :

PhysicsMechanics

parallel

$text A linear impulse end text integral F d t text acts at a point end text straight C text of the smooth end text rod invisible function application AB text . The value of end text straight x text is so that the end end text A space r e m a i n s space s t a t i o n a r y space j u s t space a f t e r space t h e space i m p a c t space i s space colon$

$text A linear impulse end text integral F d t text acts at a point end text straight C text of the smooth end text rod invisible function application AB text . The value of end text straight x text is so that the end end text A space r e m a i n s space s t a t i o n a r y space j u s t space a f t e r space t h e space i m p a c t space i s space colon$

PhysicsMechanics

A homogeneous rod AB of length L and mass M is hinged at the centre O in such a way that it can rotate freely in the vertical plane. The rod is initially in horizontal position. An insect S of the same mass M falls vertically with speed V on point C, midway between the points O and B. Immediately after falling, the insect starts to move towards B such that the rod rotates with a constant angular velocity $omega$ .

If insect reaches the end B when the rod has turned through an angle of calculate V in terms of L

A homogeneous rod AB of length L and mass M is hinged at the centre O in such a way that it can rotate freely in the vertical plane. The rod is initially in horizontal position. An insect S of the same mass M falls vertically with speed V on point C, midway between the points O and B. Immediately after falling, the insect starts to move towards B such that the rod rotates with a constant angular velocity $omega$ .

If insect reaches the end B when the rod has turned through an angle of calculate V in terms of L

PhysicsMechanics

A homogeneous rod AB of length L and mass M is hinged at the centre O in such a way that it can rotate freely in the vertical plane. The rod is initially in horizontal position. An insect S of the same mass M falls vertically with speed V on point C, midway between the points O and B. Immediately after falling, the insect starts to move towards B such that the rod rotates with a constant angular velocity $omega$ .

Calculate angular velocity in terms of V and L

A homogeneous rod AB of length L and mass M is hinged at the centre O in such a way that it can rotate freely in the vertical plane. The rod is initially in horizontal position. An insect S of the same mass M falls vertically with speed V on point C, midway between the points O and B. Immediately after falling, the insect starts to move towards B such that the rod rotates with a constant angular velocity $omega$ .

Calculate angular velocity in terms of V and L

PhysicsMechanics

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