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Physics

Mechanics

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Question

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

$6 M L^{2}$
$\frac{4}{3} M L^{2}$
$\frac{8}{3} M L^{2}$
$\frac{10}{3} M L^{2}$

The correct answer is: $8 over 3 M L squared$

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

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

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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

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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

parallel

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

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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

parallel

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