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Physics

Mechanics

Easy

Question

$A space r i g i d space b o d y space o f space m o m e n t space o f space i n e r t i a l space I space i s space p r o j e c t e d space w i t h space v e l o c i t y space V space m a k i n g space a n space a n g l e space o f space space space w i t h space h o r i z o n t a l. space T h e space m a g n i t u d e space o f space a n g u l a r space m o m e n t u m space o f space t h e space p r o j e c t i l e space a b o u t space t h e space p o i n t space o f space p r o j e c t i o n space text when the body is at its maximum height is given by end text fraction numerator I V cubed over denominator 2 square root of 2 g R squared end fraction text where end text straight R text is the radius of the rigid end text b o d y. space T h e space r i g i d space b o d y space i s colon$

sphere
spherical shell
disc
none of these

The correct answer is: disc

$text At highest point, velocity end text equals V cos invisible function application 45 to the power of ring operator equals V divided by square root of 2 L equals m fraction numerator V over denominator square root of 2 end fraction times r perpendicular text Here end text r subscript perpendicular equals h equals fraction numerator V squared sin squared invisible function application 45 to the power of ring operator over denominator 2 g end fraction equals fraction numerator V squared over denominator 4 g end fraction table attributes columnalign left columnspacing 1em rowspacing 4 pt end attributes row cell L equals fraction numerator m V cubed over denominator 4 square root of 2 g end fraction equals fraction numerator I V cubed over denominator 2 square root of 2 g R squared end fraction left parenthesis text given end text right parenthesis end cell row cell text So end text comma m over 2 equals I over R squared end cell row cell I equals 1 half m R squared end cell end table I t space i s space a space d i s c$

Related Questions to study

A cubical block of side L and mass m is placed on a horizontal floor. In the arrangement as shown, a force F is applied at the end of the plane sheet PQ which is firmly attached with the block. What should be the minimum value of PQ so that block may be tipped about an edge?

A cubical block of side L and mass m is placed on a horizontal floor. In the arrangement as shown, a force F is applied at the end of the plane sheet PQ which is firmly attached with the block. What should be the minimum value of PQ so that block may be tipped about an edge?

PhysicsMechanics

$A space h e m i s p h e r i c a l space s h e l l space o f space m a s s space M space a n d space r a d i u s space R space i s space h i n g e d space a t space p o i n t space O space a n d space p l a c e d space o n space a space h o r i z o n t a l space text surface. A ball of mass M moving with a velocity u inclined at an angle end text theta equals tan to the power of negative 1 end exponent invisible function application open parentheses 1 half close parentheses text strikes end text text the shell at point A (as shown in the figure) and stops. What is the minimum speed u if the end text text given shell is to reach the horizontal surface OP? end text$

$A space h e m i s p h e r i c a l space s h e l l space o f space m a s s space M space a n d space r a d i u s space R space i s space h i n g e d space a t space p o i n t space O space a n d space p l a c e d space o n space a space h o r i z o n t a l space text surface. A ball of mass M moving with a velocity u inclined at an angle end text theta equals tan to the power of negative 1 end exponent invisible function application open parentheses 1 half close parentheses text strikes end text text the shell at point A (as shown in the figure) and stops. What is the minimum speed u if the end text text given shell is to reach the horizontal surface OP? end text$

PhysicsMechanics

A particle moves in a circular path with decreasing speed. Choose the correct statement

A particle moves in a circular path with decreasing speed. Choose the correct statement

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A thin wire of length L and uniform linear mass density is bent into a circular loop with centre at O as shown. The moment of inertia of the loop about the axis XX’ is :

A thin wire of length L and uniform linear mass density is bent into a circular loop with centre at O as shown. The moment of inertia of the loop about the axis XX’ is :

PhysicsMechanics

The free end of a thread wound on a bobbin is passed round a nail A hammered into the wall. The thread is pulled at a constant velocity ’v’ Assuming pure rolling of bobbin, find the velocity $v subscript 0$ of the centre of the bobbin at the instant when the thread forms an angle with the vertical: (R and r are outer and inner radii off the bobbin)

The free end of a thread wound on a bobbin is passed round a nail A hammered into the wall. The thread is pulled at a constant velocity ’v’ Assuming pure rolling of bobbin, find the velocity $v subscript 0$ of the centre of the bobbin at the instant when the thread forms an angle with the vertical: (R and r are outer and inner radii off the bobbin)

PhysicsMechanics

A ball is attached to a string that is attached to a thick pole. When the ball is hit, the string warps around the pole and the ball spirals inwards sliding on the frictionless surface. Neglecting air resistance, what happens as the ball swings around the pole?

A ball is attached to a string that is attached to a thick pole. When the ball is hit, the string warps around the pole and the ball spirals inwards sliding on the frictionless surface. Neglecting air resistance, what happens as the ball swings around the pole?

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parallel

A particle P collides elastically at M with a speed v. The change in angular momentum of the particle about the point N during collision is :

A particle P collides elastically at M with a speed v. The change in angular momentum of the particle about the point N during collision is :

PhysicsMechanics

A disc of mass m is connected with an ideal spring of stiffness k. If it is released from rest., it rolls without sliding on an inclined plane. The maximum elongation of the spring is :

A disc of mass m is connected with an ideal spring of stiffness k. If it is released from rest., it rolls without sliding on an inclined plane. The maximum elongation of the spring is :

PhysicsMechanics

A uniform cylinder of mass m is kept on an accelerating wedge. If the wedge moves with an acceleration $a equals 3 g tan invisible function application theta$ , the minimum coefficient of friction between the cylinder and wedge to avoid relative sliding between them is

A uniform cylinder of mass m is kept on an accelerating wedge. If the wedge moves with an acceleration $a equals 3 g tan invisible function application theta$ , the minimum coefficient of friction between the cylinder and wedge to avoid relative sliding between them is

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parallel

A rod touches a disc kept on a smooth horizontal plane. If the rod moves with an acceleration a, the disc rolls on the rod without sliding. Then, the acceleration of the disc w.r.t the rod is

A rod touches a disc kept on a smooth horizontal plane. If the rod moves with an acceleration a, the disc rolls on the rod without sliding. Then, the acceleration of the disc w.r.t the rod is

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A uniform box is kept on a rough inclined plane. It begins to topple when $theta$ is equal to:

A uniform box is kept on a rough inclined plane. It begins to topple when $theta$ is equal to:

PhysicsMechanics

A rigid massless beam is balanced by a particle of mass 4m in left hand side and a pulley particle system in right hand side. The value of x/y is:

A rigid massless beam is balanced by a particle of mass 4m in left hand side and a pulley particle system in right hand side. The value of x/y is:

PhysicsMechanics

parallel

$straight A space uniform space rod space of space mass space straight M equals 2 kg space and space length space straight L space is space suspended space by space two space smooth space hinges space 1 space and space 2 space as space shown space in space figure. space straight A space force space straight F equals 4 straight N space is space applied space downward space at space straight a space distance space straight L divided by 4 space from space hinge space 2. space Due space to space the space application space of space force space straight F comma space hinge space 2 space breaks. space At space this space instant space comma space applied space force space straight F space is space also space removed. space The space rod space starts space to space rotate space downward space about space hinge space 1. space open parentheses g equals 10 m divided by s squared close parentheses$

$The space reaction space at space hinge space 1 comma space just space after space breaking space of space hinge space 2 comma space is space$

$straight A space uniform space rod space of space mass space straight M equals 2 kg space and space length space straight L space is space suspended space by space two space smooth space hinges space 1 space and space 2 space as space shown space in space figure. space straight A space force space straight F equals 4 straight N space is space applied space downward space at space straight a space distance space straight L divided by 4 space from space hinge space 2. space Due space to space the space application space of space force space straight F comma space hinge space 2 space breaks. space At space this space instant space comma space applied space force space straight F space is space also space removed. space The space rod space starts space to space rotate space downward space about space hinge space 1. space open parentheses g equals 10 m divided by s squared close parentheses$

$The space reaction space at space hinge space 1 comma space just space after space breaking space of space hinge space 2 comma space is space$

PhysicsMechanics

$straight A space uniform space rod space of space mass space straight M equals 2 kg space and space length space straight L space is space suspended space by space two space smooth space hinges space 1 space and space 2 space as space shown space in space figure. space straight A space force space straight F equals 4 straight N space is space applied space downward space at space straight a space distance space straight L divided by 4 space from space hinge space 2. space Due space to space the space application space of space force space straight F comma space hinge space 2 space breaks. space At space this space instant space comma space applied space force space straight F space is space also space removed. space The space rod space starts space to space rotate space downward space about space hinge space 1. space open parentheses g equals 10 m divided by s squared close parentheses$

$The space reaction space at space hinge space 1 comma space before space space hinge space 2 space breaks comma space is space$

$straight A space uniform space rod space of space mass space straight M equals 2 kg space and space length space straight L space is space suspended space by space two space smooth space hinges space 1 space and space 2 space as space shown space in space figure. space straight A space force space straight F equals 4 straight N space is space applied space downward space at space straight a space distance space straight L divided by 4 space from space hinge space 2. space Due space to space the space application space of space force space straight F comma space hinge space 2 space breaks. space At space this space instant space comma space applied space force space straight F space is space also space removed. space The space rod space starts space to space rotate space downward space about space hinge space 1. space open parentheses g equals 10 m divided by s squared close parentheses$

$The space reaction space at space hinge space 1 comma space before space space hinge space 2 space breaks comma space is space$

PhysicsMechanics

$straight A space body space of space mass space straight M space and space radius space straight R space is space as space shown space in space figure space. space The space body space can space be space straight a space ring space comma space straight a space disc comma space straight a space hollow space sphere space or space straight a space solid space I subscript x comma I subscript y. space space and space I subscript z space space are space the space moments space of space inertia space about space straight x comma straight y space and space straight z space axis space respectively. space Origin space coincides space with space centre space of space mass space of space the space body.$

Column I
Column II

i. $I subscript x equals I subscript y equals I subscript z$
a. possible for ring or disc

ii. $I subscript x equals I subscript y plus I subscript z$
b. possible for hollow sphere or solid sphere

iii. $I subscript y equals I subscript z plus I subscript x$
c. possible for all of the bodies mentioned

iv. $I subscript z equals I subscript x plus I subscript y$
d. not possible for any of the body mentioned

$straight A space body space of space mass space straight M space and space radius space straight R space is space as space shown space in space figure space. space The space body space can space be space straight a space ring space comma space straight a space disc comma space straight a space hollow space sphere space or space straight a space solid space I subscript x comma I subscript y. space space and space I subscript z space space are space the space moments space of space inertia space about space straight x comma straight y space and space straight z space axis space respectively. space Origin space coincides space with space centre space of space mass space of space the space body.$

Column I
Column II

i. $I subscript x equals I subscript y equals I subscript z$
a. possible for ring or disc

ii. $I subscript x equals I subscript y plus I subscript z$
b. possible for hollow sphere or solid sphere

iii. $I subscript y equals I subscript z plus I subscript x$
c. possible for all of the bodies mentioned

iv. $I subscript z equals I subscript x plus I subscript y$
d. not possible for any of the body mentioned

PhysicsMechanics

parallel

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