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Physics

Mechanics

Easy

Question

A force of $left parenthesis 2 i with hat on top minus 4 j with hat on top plus 2 k with hat on top right parenthesis$ Newton acts at a point $left parenthesis 3 i with hat on top plus 2 j with hat on top minus 4 k with hat on top right parenthesis$ metre from the origin. The magnitude of torque is -

zero
24.4 N-m
0.244 N-m
2.444 N-m

The correct answer is: 24.4 N-m

$F with rightwards arrow on top equals left parenthesis 2 i with hat on top minus 4 j with hat on top plus 2 k with hat on top space right parenthesis r with rightwards arrow on top equals left parenthesis 3 i with hat on top plus 2 j with hat on top minus 4 k with hat on top space right parenthesis T o r q u e space equals space r with rightwards arrow on top cross times F with rightwards arrow on top$
$vertical line left parenthesis 3 i with not stretchy hat on top plus 2 j with not stretchy hat on top minus 4 k with not stretchy hat on top right parenthesis cross times left parenthesis 2 i with not stretchy hat on top minus 4 j with not stretchy hat on top plus 2 k with not stretchy hat on top right parenthesis vertical line$
$open vertical bar table row i j k row 3 2 cell negative 4 end cell row 2 cell negative 4 end cell 2 end table close vertical bar$
$i with not stretchy hat on top left parenthesis 4 minus 16 right parenthesis minus j with not stretchy hat on top left parenthesis 6 plus 8 right parenthesis plus k with not stretchy hat on top left parenthesis negative 12 minus 4 right parenthesis$
$equals vertical line minus 12 i with not stretchy hat on top minus 14 j with not stretchy hat on top minus 16 k with not stretchy hat on top vertical line$
$equals square root of left parenthesis 12 right parenthesis squared plus left parenthesis 14 right parenthesis squared plus left parenthesis negative 16 right parenthesis squared end root equals 24.4 N minus m$

Related Questions to study

A disc is rotating with an angular velocity $omega$ ₀. A constant retarding torque is applied on it to stop the disc. The angular velocity becomes ( $omega$ ₀/2) after n rotations. How many more rotations will it make before coming to rest?

A disc is rotating with an angular velocity $omega$ ₀. A constant retarding torque is applied on it to stop the disc. The angular velocity becomes ( $omega$ ₀/2) after n rotations. How many more rotations will it make before coming to rest?

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A beam of length $l$ lies on the +x axis with its left end on the origin. A cable pulls the beam in y-direction with a force $straight F equals straight F subscript 0 left parenthesis 1 minus straight x over ell right parenthesis$ .If the axis is fixed at x = 0 then find the torque

A beam of length $l$ lies on the +x axis with its left end on the origin. A cable pulls the beam in y-direction with a force $straight F equals straight F subscript 0 left parenthesis 1 minus straight x over ell right parenthesis$ .If the axis is fixed at x = 0 then find the torque

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The magnitude of torque with respect to origin, acting on the particle at t = 1s will be

The magnitude of torque with respect to origin, acting on the particle at t = 1s will be

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The position vector of a body of mass m = 4 kg is given as $r with not stretchy rightwards arrow on top equals i with hat on top left parenthesis t squared minus 4 t right parenthesis plus j with hat on top left parenthesis negative t cubed right parenthesis$ where $r with rightwards arrow on top$ is in metres and t in seconds. The magnitude of force $open parentheses F with rightwards arrow on top close parentheses$ acting on particle at t = 1s is

The position vector of a body of mass m = 4 kg is given as $r with not stretchy rightwards arrow on top equals i with hat on top left parenthesis t squared minus 4 t right parenthesis plus j with hat on top left parenthesis negative t cubed right parenthesis$ where $r with rightwards arrow on top$ is in metres and t in seconds. The magnitude of force $open parentheses F with rightwards arrow on top close parentheses$ acting on particle at t = 1s is

PhysicsMechanics

An equilateral triangle ABC has its centre at O as shown in figure. Three forces 10 N, 5N and F are acting along the sides AB, BC and AC. Magnitude of F so that the net torque about ‘O’ is zero is

An equilateral triangle ABC has its centre at O as shown in figure. Three forces 10 N, 5N and F are acting along the sides AB, BC and AC. Magnitude of F so that the net torque about ‘O’ is zero is

PhysicsMechanics

When a steady torque (net force is zero) is acting on a body, the body

When a steady torque (net force is zero) is acting on a body, the body

PhysicsMechanics

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$W h e n space a space t o r q u e space a c t i n g space u p o n space a space s y s t e m space i s space z e r o comma space w h i c h space o f space t h e space f o l l o w i n g space w i l l space b e space c o n s tan t ?$

$W h e n space a space t o r q u e space a c t i n g space u p o n space a space s y s t e m space i s space z e r o comma space w h i c h space o f space t h e space f o l l o w i n g space w i l l space b e space c o n s tan t ?$

PhysicsMechanics

$text A couple produces end text$

$text A couple produces end text$

PhysicsMechanics

$T w o space p a r t i c l e s space A space a n d space B space a r e space s i t u a t e d space a t space a space d i s tan c e space d equals 2 space m space a p a r t. space P a r t i c l e space A space h a s space a space v e l o c i t y space o f space 10 space m space divided by space s space a t space a n space a n g l e space o f space 60 to the power of 0 space a n d space p a r t i c l e space B space h a s space a space v e l o c i t y space v space a t space a n space a n g l e 30 to the power of 0 space a s space s h o w n space i n space f i g u r e. space T h e space d i s tan c e space d space b e t w e e n space A space a n d space B space i s space c o n s tan t. space T h e space a n g u l a r space v e l o c i t y space o f space B space w i t h space r e s p e c t space t o space A space i s colon$

$T w o space p a r t i c l e s space A space a n d space B space a r e space s i t u a t e d space a t space a space d i s tan c e space d equals 2 space m space a p a r t. space P a r t i c l e space A space h a s space a space v e l o c i t y space o f space 10 space m space divided by space s space a t space a n space a n g l e space o f space 60 to the power of 0 space a n d space p a r t i c l e space B space h a s space a space v e l o c i t y space v space a t space a n space a n g l e 30 to the power of 0 space a s space s h o w n space i n space f i g u r e. space T h e space d i s tan c e space d space b e t w e e n space A space a n d space B space i s space c o n s tan t. space T h e space a n g u l a r space v e l o c i t y space o f space B space w i t h space r e s p e c t space t o space A space i s colon$

PhysicsMechanics

parallel

$A space h o o p space r o l l s space o n space a space h o r i z o n t a l space g r o u n d space w i t h o u t space s l i p p i n g space w i t h space l i n e a r space s p e e d space v. space S p e e d space o f space a space p a r t i c l e space P space o n space t h e space c i r c u m f e r e n c e space o f space t h e space h o o p space a t space a n g l e space theta space i s colon$

$A space h o o p space r o l l s space o n space a space h o r i z o n t a l space g r o u n d space w i t h o u t space s l i p p i n g space w i t h space l i n e a r space s p e e d space v. space S p e e d space o f space a space p a r t i c l e space P space o n space t h e space c i r c u m f e r e n c e space o f space t h e space h o o p space a t space a n g l e space theta space i s colon$

PhysicsMechanics

$I n space f i g u r e comma space w h e e l space A space o f space r a d i u s space r subscript A equals 10 space c m space i s space c o u p l e d space b y space b e l t space B space t o space w h e e l space C space o f space r a d i u s space r subscript C equals space 25 space c m. space T h e space a n g u l a r space s p e e d space o f space w h e e l space A space i s space i n c r e a s e d space f r o m space r e s t space a t a space c o n s tan t space r a t e space o f space 1.6 space r a d space divided by space s squared. space F i n d space t h e space t i m e space n e e d e d space f o r space w h e e l space C space t o space r e a c h space a n space a n g u l a r space s p e e d space o f space 12.8 space r a d space divided by space s comma space a s s u m i n g space t h e space b e l t space d o e s space n o t space s l i p.$

$I n space f i g u r e comma space w h e e l space A space o f space r a d i u s space r subscript A equals 10 space c m space i s space c o u p l e d space b y space b e l t space B space t o space w h e e l space C space o f space r a d i u s space r subscript C equals space 25 space c m. space T h e space a n g u l a r space s p e e d space o f space w h e e l space A space i s space i n c r e a s e d space f r o m space r e s t space a t a space c o n s tan t space r a t e space o f space 1.6 space r a d space divided by space s squared. space F i n d space t h e space t i m e space n e e d e d space f o r space w h e e l space C space t o space r e a c h space a n space a n g u l a r space s p e e d space o f space 12.8 space r a d space divided by space s comma space a s s u m i n g space t h e space b e l t space d o e s space n o t space s l i p.$

PhysicsMechanics

$S u p p o s e space a space c a r apostrophe s space s tan d a r d space t i r e s space a r e space r e p l a c e d space w i t h space t i r e s space 1.50 space t i m e s space l a r g e r space i n space d i a m e t e r. space W i l l space t h e space c a r apostrophe s space s p e e d o m e t e r space r e a d i n g space b e$

$S u p p o s e space a space c a r apostrophe s space s tan d a r d space t i r e s space a r e space r e p l a c e d space w i t h space t i r e s space 1.50 space t i m e s space l a r g e r space i n space d i a m e t e r. space W i l l space t h e space c a r apostrophe s space s p e e d o m e t e r space r e a d i n g space b e$

PhysicsMechanics

parallel

$W h e n space a space p e r s o n space t h r o w s space a space m e t e r space s t i c k space i t space i s space f o u n d space t h a t space t h e space c e n t r e space o f space t h e space s t i c k space i s m o v i n g space w i t h space s p e e d space 10 space m divided by s space a n d space l e f t space e n d space o f space s t i c k space w i t h space s p e e d space 20 space m divided by s. space B o t h space p o i n t s space m o v e space v e r t i c a l l y space u p w a r d s space a t space t h a t space m o m e n t. space T h e n space a n g u l a r space s p e e d space o f space t h e s t i c k space i s colon$

$W h e n space a space p e r s o n space t h r o w s space a space m e t e r space s t i c k space i t space i s space f o u n d space t h a t space t h e space c e n t r e space o f space t h e space s t i c k space i s m o v i n g space w i t h space s p e e d space 10 space m divided by s space a n d space l e f t space e n d space o f space s t i c k space w i t h space s p e e d space 20 space m divided by s. space B o t h space p o i n t s space m o v e space v e r t i c a l l y space u p w a r d s space a t space t h a t space m o m e n t. space T h e n space a n g u l a r space s p e e d space o f space t h e s t i c k space i s colon$

PhysicsMechanics

$text A moving particle of mass end text m text collides head-on with a particle of mass end text 2 m text which is end text table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em rowspacing 3 pt end attributes row blank row cell text initially at rest. Fraction of kinetic energy retained by end text m comma text after the collision end text end cell end table$

$text A moving particle of mass end text m text collides head-on with a particle of mass end text 2 m text which is end text table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em rowspacing 3 pt end attributes row blank row cell text initially at rest. Fraction of kinetic energy retained by end text m comma text after the collision end text end cell end table$

PhysicsMechanics

$text A end text 1 Kg text ball moving at end text 12 ms to the power of negative 1 end exponent text collides with a end text 2 Kg text ball moving in the opposite end text text direction at end text 24 ms to the power of negative 1 end exponent text . If the coefficient of restitution is end text 2 divided by 3 comma text their velocities after end text text impact are end text$

$text A end text 1 Kg text ball moving at end text 12 ms to the power of negative 1 end exponent text collides with a end text 2 Kg text ball moving in the opposite end text text direction at end text 24 ms to the power of negative 1 end exponent text . If the coefficient of restitution is end text 2 divided by 3 comma text their velocities after end text text impact are end text$

PhysicsMechanics

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