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Physics

Mechanics

Easy

Question

Two particles A and B of mass m each, are joined by a rigid massless rod of length l. A particle P of mass m, moving with speed u normal to AB, strikes A and stick to it. The centre of mass of the 'A + B + P' system after collision is C. If u = 4m/s, m = 3 kg, l = 3 m, then (All quantities in column are in SI units)

$i \to c; i i \to b; i i i \to a; i v \to a$
$i \to d_{i} i i \to a_{i} i i i \to a_{;} i v \to b$
$i \to c_{, i i} \to a_{;} i i i \to a_{;}, i v \to b$
$i \to a, i i \to d; i i i \to b; i v \to c$

The correct answer is: $i not stretchy rightwards arrow d subscript i i i not stretchy rightwards arrow a subscript i i i i not stretchy rightwards arrow a subscript semicolon i v not stretchy rightwards arrow b$

Related Questions to study

$In space Column space straight I comma space information space about space the space force left parenthesis straight s right parenthesis space acting space on space straight a space body space is space mentioned comma space while space in space Column space II space information space about space the space motion space of space straight a space body space is space given. space Match space the space entries space in space Column space II space with space the space entries space in space Column space straight I.$

Column I
Column II

i. A single force through centre of mass
a. Rotational motion

ii.Equal and opposite forces separated by non-zero distance
b. Translation motion

iii. Equal and opposite forces acting at the same point
c. No motion

iv. A single force not through centre of mass
d. Centre of mass performs translatory motion

$In space Column space straight I comma space information space about space the space force left parenthesis straight s right parenthesis space acting space on space straight a space body space is space mentioned comma space while space in space Column space II space information space about space the space motion space of space straight a space body space is space given. space Match space the space entries space in space Column space II space with space the space entries space in space Column space straight I.$

Column I
Column II

i. A single force through centre of mass
a. Rotational motion

ii.Equal and opposite forces separated by non-zero distance
b. Translation motion

iii. Equal and opposite forces acting at the same point
c. No motion

iv. A single force not through centre of mass
d. Centre of mass performs translatory motion

PhysicsMechanics

$From space straight a space uniform space disc space of space mass space straight M space and space radius space straight R comma space straight a space concentric space disc space of space radius space straight R divided by 2 space is space cut space out. space For space the space remaining space space annular space disc colon I subscript 1 space space space is space the space moment space of space inertia space about space axis space ‘ 1 ’ comma space space I subscript 2 space about space ‘ 2 ’ comma space space space space I subscript 3 italic space about space space ‘ 3 ’ comma space and space I subscript 4 space space space about space ‘ 4 ’. space Axes space ‘ 1 ’ space and space ‘ 2 ’ space are space perpendicular space to space the space disc space and space ‘ 3 ’ space and space ‘ 4 ’ space are space in space the space plane space of space the space disc. space Axes space ‘ 2 ’ comma ’ 3 ’ space and space ‘ 4 ’ space intersect space at space straight a space common space point. space Match space the space following space$

Column – I

Column – II

i. $I subscript 1$ is equal to
a. $21 over 32 M R squared$

ii. $I subscript 2$ is equal to
b. $I subscript 1 divided by 2$

iii. $I subscript 3 plus I subscript 4$ is equal to
c. $15 over 32 M R h 2$

iv. $I subscript 2 minus I subscript 3$ is equal to
d. none of these

$From space straight a space uniform space disc space of space mass space straight M space and space radius space straight R comma space straight a space concentric space disc space of space radius space straight R divided by 2 space is space cut space out. space For space the space remaining space space annular space disc colon I subscript 1 space space space is space the space moment space of space inertia space about space axis space ‘ 1 ’ comma space space I subscript 2 space about space ‘ 2 ’ comma space space space space I subscript 3 italic space about space space ‘ 3 ’ comma space and space I subscript 4 space space space about space ‘ 4 ’. space Axes space ‘ 1 ’ space and space ‘ 2 ’ space are space perpendicular space to space the space disc space and space ‘ 3 ’ space and space ‘ 4 ’ space are space in space the space plane space of space the space disc. space Axes space ‘ 2 ’ comma ’ 3 ’ space and space ‘ 4 ’ space intersect space at space straight a space common space point. space Match space the space following space$

Column – I

Column – II

i. $I subscript 1$ is equal to
a. $21 over 32 M R squared$

ii. $I subscript 2$ is equal to
b. $I subscript 1 divided by 2$

iii. $I subscript 3 plus I subscript 4$ is equal to
c. $15 over 32 M R h 2$

iv. $I subscript 2 minus I subscript 3$ is equal to
d. none of these

PhysicsMechanics

$End space straight A space space of space straight a space rod space AB space is space being space pulled space on space the space floor space with space straight a space constant space velocity space space v subscript 0 space as space shown. space Taking space the space length space of the space rod space as space l space comma space at space an space instant space when space the space rod space makes space an space angle space 37 to the power of 0 space space with space the space horizontal comma space calculate space space$

$The space angular space velocity space of space the space end space$

$End space straight A space space of space straight a space rod space AB space is space being space pulled space on space the space floor space with space straight a space constant space velocity space space v subscript 0 space as space shown. space Taking space the space length space of the space rod space as space l space comma space at space an space instant space when space the space rod space makes space an space angle space 37 to the power of 0 space space with space the space horizontal comma space calculate space space$

$The space angular space velocity space of space the space end space$

PhysicsMechanics

parallel

$End space straight A space space of space straight a space rod space AB space is space being space pulled space on space the space floor space with space straight a space constant space velocity space space v subscript 0 space as space shown. space Taking space the space length space of the space rod space as space space comma space at space an space instant space when space the space rod space makes space an space angle space 37 to the power of 0 space space with space the space horizontal comma space calculate$

$The space velocity space of space end space straight B$

$End space straight A space space of space straight a space rod space AB space is space being space pulled space on space the space floor space with space straight a space constant space velocity space space v subscript 0 space as space shown. space Taking space the space length space of the space rod space as space space comma space at space an space instant space when space the space rod space makes space an space angle space 37 to the power of 0 space space with space the space horizontal comma space calculate$

$The space velocity space of space end space straight B$

PhysicsMechanics

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

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The horizontal and vertical components of the force exerted on the beam at the wall

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The horizontal and vertical components of the force exerted on the beam at the wall

PhysicsMechanics

parallel

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The tension in the cable

$The space horizontal space beam space in space figure space weighs space 150 straight N comma space and space its space centre space of space gravity space is space at space its space centre. space Find space$

The tension in the cable

PhysicsMechanics

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$Four space spheres space of space diameter space 2 straight a space and space mass space straight M space are space placed space with space their space centres space on space the space four space corners space of space straight a space square space of space side space straight b. space Then space the space moment space of space Inertia space of space the space system space about space an space axis space along space one space of space the space sides space of space the space square space is space$

PhysicsMechanics

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$straight A space recording space disc space rotates space steadily space at space 45 space rev divided by min space on space straight a space table. space When space straight a space small space mass space of space 0.02 space kg space is space dropped space gently space on space the space disc space at space straight a space distance space of space 0.04 space straight m space from space its space axis space and space stucks space to space the space disc comma space the space rate space of space revolution space falls space to space 36 space rev divided by min. space The space moment space of space inertia space of space the space disc space about space its space centre space is space$

PhysicsMechanics

parallel

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PhysicsMechanics

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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

parallel

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

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PhysicsMechanics

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PhysicsMechanics

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PhysicsMechanics

parallel

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