Have a query? Ask a Tutor!!

Access to best educators and exclusive paper discussions

Offsite Campus Turito Championship

Can’t find what you’re looking for?

Our tutors are from top schools around the world, and they are waiting for you 24/7, anytime, anywhere.

Homework- One to One Solutions
Understand concepts to solve better
Get your doubts solved instantly

Physics

Mechanics

Easy

Question

A uniform circular disc has radius R and mass m. A particle also of mass m is fixed at a point A on the edge of the disc as shown in the figure. The disc can rotate freely about a fixed horizontal chord P Q that is at a distance R/4 from the center C of the disc. The line AC is perpendicular of P Q. Initially, the disc is held vertical with the point A at its highest position. It is then allowed to fall so that it starts rotating about P Q. Find the linear speed of the particle as it reaches its lowest position.

$\sqrt{g R}$
$\sqrt{5 g R}$
$\sqrt{5 R}$

The correct answer is: $square root of 5 g R end root$

$table attributes columnalign left columnspacing 1em rowspacing 4 pt end attributes row cell m g open parentheses R plus R over 4 close parentheses plus m g R over 4 equals negative m g open parentheses R plus R over 4 close parentheses minus m g R over 4 plus 1 half I subscript P Q end subscript omega squared 3 m g R equals 1 half I subscript P Q end subscript omega squared end cell row cell I subscript P Q end subscript equals m open parentheses R plus R over 4 close parentheses squared plus open square brackets 1 fourth m R squared plus m open parentheses R over 4 close parentheses squared close square brackets equals 15 over 8 m R squared end cell end table table attributes columnalign left columnspacing 1em rowspacing 4 pt end attributes row cell 3 m g R equals 1 half cross times 15 over 8 m R squared omega squared not stretchy rightwards double arrow omega equals square root of fraction numerator 16 g over denominator 5 R end fraction end root end cell row cell v equals open parentheses R plus R over 4 close parentheses omega equals fraction numerator 5 R over denominator 4 end fraction square root of fraction numerator 16 g over denominator 5 R end fraction end root equals square root of 5 g R end root end cell end table$

Related Questions to study

A particle of mass m is released from rest at point A which falls parallel to the vertical direction. Angular momentum of that particle as function of time t with respect to origin o is

A particle of mass m is released from rest at point A which falls parallel to the vertical direction. Angular momentum of that particle as function of time t with respect to origin o is

PhysicsMechanics

$A space u n i f o r m space r o d space A space B space o f space m a s s space m space a n d space l e n g t h space L space i s space a t space r e s t space o n space a space s m o o t h space h o r i z o n t a l space s u r f a c e. space A n space i m p u l s e space text J is applied to the end end text straight B text perpendicular to the rod is horizontal direction. Speed of point end text straight P text at a end text text distance end text L over 6 text from the centre towards end text straight A text of the rod after time end text t equals fraction numerator pi m L over denominator 12 J end fraction text is end text$

$A space u n i f o r m space r o d space A space B space o f space m a s s space m space a n d space l e n g t h space L space i s space a t space r e s t space o n space a space s m o o t h space h o r i z o n t a l space s u r f a c e. space A n space i m p u l s e space text J is applied to the end end text straight B text perpendicular to the rod is horizontal direction. Speed of point end text straight P text at a end text text distance end text L over 6 text from the centre towards end text straight A text of the rod after time end text t equals fraction numerator pi m L over denominator 12 J end fraction text is end text$

PhysicsMechanics

Two particles each of mass m are attached at the ends of a massless rod of length L which is on a smooth table at rest. An impulse J is applied to one particle along a direction perpendicular to the length of the rod. Immediately after that, angular velocity of the rod would be

Two particles each of mass m are attached at the ends of a massless rod of length L which is on a smooth table at rest. An impulse J is applied to one particle along a direction perpendicular to the length of the rod. Immediately after that, angular velocity of the rod would be

PhysicsMechanics

parallel

A thin uniform rod of mass m and length L is force to rotate about its upper and when it is at rest, it receives an impulse J at its lowest point, normal to its length. immediately, after impact

A thin uniform rod of mass m and length L is force to rotate about its upper and when it is at rest, it receives an impulse J at its lowest point, normal to its length. immediately, after impact

PhysicsMechanics

$text A particular of mass end text m equals 5 text is moving with a uniform speed end text v equals 3 square root of 2 text in the XOY plane along the line end text Y equals X plus 4 T h e space m a g n i t u d e space o f space t h e space a n g u l a r space m o m e n t u m space o f space t h e space p a r t i c l e space a b o u t space t h e space o r i g i n space i s$

$text A particular of mass end text m equals 5 text is moving with a uniform speed end text v equals 3 square root of 2 text in the XOY plane along the line end text Y equals X plus 4 T h e space m a g n i t u d e space o f space t h e space a n g u l a r space m o m e n t u m space o f space t h e space p a r t i c l e space a b o u t space t h e space o r i g i n space i s$

PhysicsMechanics

A stone is whirled along a circle with a constant angular velocity and its angular momentum is L. If the radius of its circular path is halved while keeping the angular velocity same, its new angular momentum would be

A stone is whirled along a circle with a constant angular velocity and its angular momentum is L. If the radius of its circular path is halved while keeping the angular velocity same, its new angular momentum would be

PhysicsMechanics

parallel

A uniform rod of mass m and length 2l is rotating about an axis passing through its centre and perpendicular to its length. If is its angular velocity, its angular momentum about that axis is

A uniform rod of mass m and length 2l is rotating about an axis passing through its centre and perpendicular to its length. If is its angular velocity, its angular momentum about that axis is

PhysicsMechanics

$text A uniform circular disc of mass end text straight M text and radius end text straight R text rolls without slipping on a horizontal surface end text text If the velocity of its centre is end text v subscript 0 comma text then the total angular momentum of the disc about a fixed end text text point end text P text at a height end text 3 straight R divided by 2 text about the centre end text straight C text . end text$

$text A uniform circular disc of mass end text straight M text and radius end text straight R text rolls without slipping on a horizontal surface end text text If the velocity of its centre is end text v subscript 0 comma text then the total angular momentum of the disc about a fixed end text text point end text P text at a height end text 3 straight R divided by 2 text about the centre end text straight C text . end text$

PhysicsMechanics

A disc of mass m and radius R moves in the X-Y plane as shown in figure. The angular momentum of the disc about the origin O at the instant shown is

A disc of mass m and radius R moves in the X-Y plane as shown in figure. The angular momentum of the disc about the origin O at the instant shown is

PhysicsMechanics

parallel

A cube of mass ‘m’ and side ‘a’ moving along with a constant speed as shown in figure. The magnitude of angular momentum of cube about z-axis would be

A cube of mass ‘m’ and side ‘a’ moving along with a constant speed as shown in figure. The magnitude of angular momentum of cube about z-axis would be

PhysicsMechanics

$text Consider a body, shown in the figure, consisting of two identical balls, each of mass M end text text connected by a light rigid rod. If an impulse end text J equals M V text is imparted to the body at one of its ends, what would be end text i t s space a n g u l a r space m o t i o n$

$text Consider a body, shown in the figure, consisting of two identical balls, each of mass M end text text connected by a light rigid rod. If an impulse end text J equals M V text is imparted to the body at one of its ends, what would be end text i t s space a n g u l a r space m o t i o n$

PhysicsMechanics

$text A shell of mass "m' is projected with velocity end text v text at an angle end text 60 to the power of ring operator text to the horizontal. When it reaches the end text text maximum height, its angular momentum with respect to point of projection is end text$

$text A shell of mass "m' is projected with velocity end text v text at an angle end text 60 to the power of ring operator text to the horizontal. When it reaches the end text text maximum height, its angular momentum with respect to point of projection is end text$

PhysicsMechanics

parallel

Angular momentum of a solid sphere about its diameter is L. If it rotates about its tangent with the same angular velocity as that in the first case, now its angular momentum will be

Angular momentum of a solid sphere about its diameter is L. If it rotates about its tangent with the same angular velocity as that in the first case, now its angular momentum will be

PhysicsMechanics

$text A constant torque acting on a uniform circular disc changes its angular momentum from end text L text to end text fraction numerator 4 L over denominator 3 end fraction text in end text 2 text seconds. Then magnitude of the torque applied is end text$

$text A constant torque acting on a uniform circular disc changes its angular momentum from end text L text to end text fraction numerator 4 L over denominator 3 end fraction text in end text 2 text seconds. Then magnitude of the torque applied is end text$

PhysicsMechanics

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

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

PhysicsMechanics

parallel

card img

With Turito Academy.

card img

With Turito Foundation.

card img

Get an Expert Advice From Turito.

Turito Academy

card img

With Turito Academy.

Test Prep

card img

With Turito Foundation.