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Physics

Mechanics

Easy

Question

Let be a force acting on a particle having position vector . Let be the torque of this force about the origin, then-

The correct answer is:

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The three similar torque (t) are acting at an angle of 120º with each other. The resultant torque will be-

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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

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

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$text A couple produces end text$

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

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

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

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

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

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

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

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

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

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

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