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Physics

Mechanics

Easy

Question

$straight A space circular space platform space is space mounted space on space straight a space vertical space frictionless space axle. space Its space radius space straight r space equals space 2 straight m space and space its space moment space of space inertia space I italic space equals space 200 space kg minus straight m squared. space It space is space initially space at space rest. space straight A space 70 space kg space man space stands space on space the space edge space of space the space platform space and space begins space to space walk space along space the space edge space at space speed space straight v subscript 0 space equals space 10 space straight m divided by straight s space relative space to space the space ground. space The space angular space velocity space of space the space platform space is space space space$

$1.2 rad / s$
$0.4 rad / s$
$2.0 rad / s$
$0.7 rad / s$

The correct answer is: $0.7 space rad divided by straight s$

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$straight A space gramophone space record space has space radius space straight r space and space mass space straight M. space It space is space rotating space with space straight a space speed space omega italic. space Two space drops space of space wax space each space of space mass space straight m space fall space on space it space at space straight a space distance space straight r divided by 2 space on space opposite space sides. space The space new space velocity space is space$

$straight A space gramophone space record space has space radius space straight r space and space mass space straight M. space It space is space rotating space with space straight a space speed space omega italic. space Two space drops space of space wax space each space of space mass space straight m space fall space on space it space at space straight a space distance space straight r divided by 2 space on space opposite space sides. space The space new space velocity space is space$

PhysicsMechanics

$Angular space momentum space of space the space particle space rotating space with space straight a space central space force space is space constant space due space to space minus space space$

$Angular space momentum space of space the space particle space rotating space with space straight a space central space force space is space constant space due space to space minus space space$

PhysicsMechanics

$When space straight a space mass space is space rotated space in space straight a space plane space about space is space fixed space point comma space its space angular space momentum space is space directed space along space the minus$

$When space straight a space mass space is space rotated space in space straight a space plane space about space is space fixed space point comma space its space angular space momentum space is space directed space along space the minus$

PhysicsMechanics

parallel

$straight A space force space space space straight F with rightwards arrow on top equals straight a i with hat on top plus 3 straight j with hat on top plus 6 straight k with hat on top space space space is space acting space at space straight a space point space space space space straight r with rightwards arrow on top equals 2 straight i with hat on top minus 6 straight j with hat on top minus 12 straight k with hat on top. space The space value space of space apostrophe straight a apostrophe space for space which space angular space momentum space about space origin space is space conserved space is space minus space$

$straight A space force space space space straight F with rightwards arrow on top equals straight a i with hat on top plus 3 straight j with hat on top plus 6 straight k with hat on top space space space is space acting space at space straight a space point space space space space straight r with rightwards arrow on top equals 2 straight i with hat on top minus 6 straight j with hat on top minus 12 straight k with hat on top. space The space value space of space apostrophe straight a apostrophe space for space which space angular space momentum space about space origin space is space conserved space is space minus space$

PhysicsMechanics

$straight A space particle space performs space uniform space circular space motion space with space angular space momentum space apostrophe straight L apostrophe. space If space the space frequency space of space particles space motion space is space halved space and space its space KE space is space doubled space then space the space angular space momentum space becomes space – space space$

$straight A space particle space performs space uniform space circular space motion space with space angular space momentum space apostrophe straight L apostrophe. space If space the space frequency space of space particles space motion space is space halved space and space its space KE space is space doubled space then space the space angular space momentum space becomes space – space space$

PhysicsMechanics

$straight A space particle space is space moved space in space straight a space circle space with space straight a space constant space angular space velocity. space Its space angular space momentum space is space straight L. space If space the space radius space of space the space circle space is space halved space keeping space the space angular space velocity space same comma space the space angular space momentum space of space the space particle space will space become space minus$

$straight A space particle space is space moved space in space straight a space circle space with space straight a space constant space angular space velocity. space Its space angular space momentum space is space straight L. space If space the space radius space of space the space circle space is space halved space keeping space the space angular space velocity space same comma space the space angular space momentum space of space the space particle space will space become space minus$

PhysicsMechanics

parallel

$straight A space smooth space tube space of space certain space mass space is space rotated space in space straight a space gravity minus free space space space and space released. space The space two space balls space shown space in space Fig. space move space towards space the space ends space of space the space tube. space For space the space whole space system comma space which space of space the space following space quantities space is space not space conserved$

$straight A space smooth space tube space of space certain space mass space is space rotated space in space straight a space gravity minus free space space space and space released. space The space two space balls space shown space in space Fig. space move space towards space the space ends space of space the space tube. space For space the space whole space system comma space which space of space the space following space quantities space is space not space conserved$

PhysicsMechanics

The minimum height of the obstacle so that the sphere can stay in equilibrium is (R is radius of the sphere)

The minimum height of the obstacle so that the sphere can stay in equilibrium is (R is radius of the sphere)

PhysicsMechanics

$A space c y l i n d e r space r e s t s space o n space a space h o r i z o n t a l space r o t a t i n g space d i s c space a s space s h o w n. space D i s tan c e space b e t w e e n space t h e space a x e s space o f space t h e space d i s c space text and cylinder is end text straight R text . Coefficient of friction between disc and cylinder is end text mu greater than D over h. text Where end text D equals 2 r text is end text text diameter of cylinder. Value of end text omega text such that cylinder falls off the disc will be end text$

$A space c y l i n d e r space r e s t s space o n space a space h o r i z o n t a l space r o t a t i n g space d i s c space a s space s h o w n. space D i s tan c e space b e t w e e n space t h e space a x e s space o f space t h e space d i s c space text and cylinder is end text straight R text . Coefficient of friction between disc and cylinder is end text mu greater than D over h. text Where end text D equals 2 r text is end text text diameter of cylinder. Value of end text omega text such that cylinder falls off the disc will be end text$

PhysicsMechanics

parallel

The maximum ratio of b/h for which the homogeneous block will slide without toppling under the action of force F. Coefficient of static friction between the block and incline is $mu$ .

The maximum ratio of b/h for which the homogeneous block will slide without toppling under the action of force F. Coefficient of static friction between the block and incline is $mu$ .

PhysicsMechanics

A horizontal force F is applied at the top of an equilateral triangular block of mass m and side L as shown. The minimum value of coefficient of friction between block and the horizontal surface to topple the block before it slides.

A horizontal force F is applied at the top of an equilateral triangular block of mass m and side L as shown. The minimum value of coefficient of friction between block and the horizontal surface to topple the block before it slides.

PhysicsMechanics

A horizontal force F is applied to a rectangular block of mass m width b and height H so that block moves with constant velocity. is coefficient of kinetic friction. If F is applied at a height H/2 as shown, value of x where line of action of resultant contact force applied by the surface on the block acts.

A horizontal force F is applied to a rectangular block of mass m width b and height H so that block moves with constant velocity. is coefficient of kinetic friction. If F is applied at a height H/2 as shown, value of x where line of action of resultant contact force applied by the surface on the block acts.

PhysicsMechanics

parallel

A cubical block of mass m and edge length L is sliding down on an inclined plane with uniform velocity. Torque due to the normal force applied by the incline on the block about its centre of mass is

A cubical block of mass m and edge length L is sliding down on an inclined plane with uniform velocity. Torque due to the normal force applied by the incline on the block about its centre of mass is

PhysicsMechanics

An isosceles right triangular plate ABC of mass m is free to rotate in vertical plane about a fixed horizontal axis through A. It is supported by a string such that the side AB is horizontal. The reaction at the support A is

An isosceles right triangular plate ABC of mass m is free to rotate in vertical plane about a fixed horizontal axis through A. It is supported by a string such that the side AB is horizontal. The reaction at the support A is

PhysicsMechanics

In the above case rod does not slip until $theta equals$

In the above case rod does not slip until $theta equals$

PhysicsMechanics

parallel

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