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Physics

Mechanics

Easy

Question

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

zero
48 Nm
64 Nm
80 Nm

The correct answer is: 80 Nm

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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

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parallel

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

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

PhysicsMechanics

$text A couple produces end text$

$text A couple produces end text$

PhysicsMechanics

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

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

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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

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

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

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

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

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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$text A railway truck of mass end text 10 to the power of 4 Kg text travelling at end text 1 ms to the power of negative 1 end exponent text collides with another of double its end text text mass moving in the opposite direction with velocity of end text 0.2 ms to the power of negative 1 end exponent text . If the trucks couple end text text automatically on collision, their common velocity in end text ms to the power of negative 1 end exponent text . end text$

$text A railway truck of mass end text 10 to the power of 4 Kg text travelling at end text 1 ms to the power of negative 1 end exponent text collides with another of double its end text text mass moving in the opposite direction with velocity of end text 0.2 ms to the power of negative 1 end exponent text . If the trucks couple end text text automatically on collision, their common velocity in end text ms to the power of negative 1 end exponent text . end text$

PhysicsMechanics

$text A moving body with a mass m end text subscript 1 text strikes a body of mass end text m subscript 2 text which is stationary. end text text Assuming perfectly elastic impact, the ratio end text m subscript 1 divided by m subscript 2 text so as to decrease the velocity of end text text first body end text 1.5 text times is end text$

$text A moving body with a mass m end text subscript 1 text strikes a body of mass end text m subscript 2 text which is stationary. end text text Assuming perfectly elastic impact, the ratio end text m subscript 1 divided by m subscript 2 text so as to decrease the velocity of end text text first body end text 1.5 text times is end text$

PhysicsMechanics

$text A body of mass end text 1 Kg text undergoes elastic collision with another body at rest and contin- end text text useto move in the original direction with end text 1 divided by 4 text th of its initial Mass of the end text o t h e r space b o d y space text end text$

$text A body of mass end text 1 Kg text undergoes elastic collision with another body at rest and contin- end text text useto move in the original direction with end text 1 divided by 4 text th of its initial Mass of the end text o t h e r space b o d y space text end text$

PhysicsMechanics

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