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Physics

Mechanics

Easy

Question

$A space p a r t i c l e space i s space m o v i n g space w i t h space c o n s tan t space v e l o c i t y space h a s space i n i t i a l space m o m e n t u m space P space i s space g i v e n space a n space i m p u l s e space o f space m a g n i t u d e space I comma space I f space t h e r e space i s space n o space c h a n g e space i s space i t s space k i n e t i c space e n e r g y space o f space t h e space p a r t i c l e space t h e n$

$angle between its initial momentum and impulse must be < 90 °$
$angle between its initial momentum and impulse must be > 90 °$
$angle between its initial momentum & impulse is 90 °$
$not possible$

The correct answer is: $text angle between its initial momentum and impulse must be end text greater than 90 degree$

$text As K.E. remains same end text P subscript i equals P subscript f text also end text p subscript f equals P subscript i plus Y P subscript f equals square root of P subscript i superscript 2 plus I squared plus 2 P subscript i I cos theta end root table attributes columnalign left end attributes row cell rightwards double arrow I equals negative 2 P subscript i cos theta end cell row cell therefore cos theta rightwards arrow negative text ve end text text i.e. end text theta greater than 90 degree end cell end table$

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PhysicsMechanics

$T h e space m a g n i t u d e space o f space t h e space f o r c e space left parenthesis i n space N right parenthesis space a c t i n g space o n space a space b o d y space v a r i e s space w i t h space t i m e space t space left parenthesis i n space m s right parenthesis space a s space s h o w n. space A B comma space B C space a n d space C D space a r e space s t r a i g h t space l i n e space s e g m e n t s. space T h e space m a g n i t u d e space o f space t h e space t o t a l space i m p u l s e space o f space t h e f o r c e space o n space t h e space b o d y space f r o m space t space equals space 4 space mu s space t o space t space equals space 16 space mu s space i s space$

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PhysicsMechanics

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PhysicsMechanics

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$I n space t h e space f i g u r e space s h o w n space a space p e n d u l u m space h a v i n g space b o b space o f space m a s s space m space equals space 1 space k g space i s space h a n g i n g space f r o m space t h e space r o o f space o f space a space b o x space o f space m a s s space M comma space k e p t space o v e r space a space s m o o t h space h o r i z o n t a l space p l a n e. space B o x space a n d space a space b l o c k space o f space m a s s space m ¢ space i s space c o n n e c t e d space b y space a space l i g h t space s t r i n g space g o i n g space o v e r space a space m a s s l e s s space l i g h t space p u l l e y. space W h e n space s y s t e m space i s space i n space m o t i o n comma space s t r i n g space m a k e s space a n g l e space 370 space f r o m space t h e space v e r t i c a l space a t space e q u i l i b r i u m space w i t h space r e s p e c t space t o space b o x. space F i n d space o u t space t h e space v a l u e space o f space m ¢ space i n space k g$

PhysicsMechanics

$A space m o n k e y space o f space m a s s space m space i s space s i t t i n g space o n space a space p l a t f o r m space o f space m a s s space M. space M o n k e y space c a n space j u m p space w i t h space a space v e l o c i t y space o f space 5 space m divided by s space m a k i n g space a n space a n g l e space 370 space w i t h space t h e space h o r i z o n t a l space w i t h space r e s p e c t space t o space p l a t f o r m. space I f space v a l u e space o f space m divided by M space i s space x space ´ space 10 to the power of – 1 end exponent comma space t o space j u m p space t h e space m o n k e y space 1 space m e t e r space w i t h space r e s p e c t space t o space t h e space g r o u n d. space F i n d space o u t space t h e space v a l u e space o f space x$

$A space m o n k e y space o f space m a s s space m space i s space s i t t i n g space o n space a space p l a t f o r m space o f space m a s s space M. space M o n k e y space c a n space j u m p space w i t h space a space v e l o c i t y space o f space 5 space m divided by s space m a k i n g space a n space a n g l e space 370 space w i t h space t h e space h o r i z o n t a l space w i t h space r e s p e c t space t o space p l a t f o r m. space I f space v a l u e space o f space m divided by M space i s space x space ´ space 10 to the power of – 1 end exponent comma space t o space j u m p space t h e space m o n k e y space 1 space m e t e r space w i t h space r e s p e c t space t o space t h e space g r o u n d. space F i n d space o u t space t h e space v a l u e space o f space x$

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PhysicsMechanics

$A space p e n d u l u m space b o b space o f space m a s s space 10 to the power of – 2 end exponent space k g space i s space r a i s e d space t o space a space h e i g h t space 0.2 space m space a n d space t h e n space r e l e a s e d. space A t space t h e space b o t t o m space o f space i t s space s w i n g comma space i t space p i c k s space u p space a space m a s s space 10 to the power of – 2 space end exponent k g. space T o space w h a t space h e i g h t space i n space c m space w i l l space t h e space c o m b i n e d space m a s s space r i s e ? space left parenthesis g space equals space 10 m divided by s squared right parenthesis$

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PhysicsMechanics

$A space p r o j e c t i l e space o f space m a s s space m space i s space t h r o w n space w i t h space v e l o c i t y space v space m a k i n g space a n space a n g l e space o f space 30 degree space w i t h space v e r t i c a l. space N e g l e c t i n g space a i r space r e s i s tan c e space t h e space m a g n i t u d e space o f space c h a n g e space i n space m o m e n t u m space b e t w e e n space t h e space s t a r t i n g space p o i n t space a n d space a t space t h e space m a x i m u m space h e i g h t space i s space$

$A space p r o j e c t i l e space o f space m a s s space m space i s space t h r o w n space w i t h space v e l o c i t y space v space m a k i n g space a n space a n g l e space o f space 30 degree space w i t h space v e r t i c a l. space N e g l e c t i n g space a i r space r e s i s tan c e space t h e space m a g n i t u d e space o f space c h a n g e space i n space m o m e n t u m space b e t w e e n space t h e space s t a r t i n g space p o i n t space a n d space a t space t h e space m a x i m u m space h e i g h t space i s space$

PhysicsMechanics

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$1. T w o space b l o c k s space o f space m a s s e s space m subscript 1 space end subscript a n d space m subscript 2 space a r e space space c o n n e c t e d space b y space a space s p r i n g space o f space s p r i n g space c o n s tan t space k. space T h e space b l o c k space o f space m a s s space m subscript 2 space i s space g i v e n space a space s h a r p space i m p u l s e space s o space t h a t space i t space a c q u i r e s space a space v e l o c i t y space v subscript 0 space t o w a r d space r i g h t. space I f space s p r i n g space b r e a k space w h e n space v e l o c i t y space o f space m subscript 2 space i s space fraction numerator 3 v subscript 0 over denominator 4 end fraction space t h e space v e l o c i t y space o f space o t h e r space b l o c k space w i l l space b e space$

$1. T w o space b l o c k s space o f space m a s s e s space m subscript 1 space end subscript a n d space m subscript 2 space a r e space space c o n n e c t e d space b y space a space s p r i n g space o f space s p r i n g space c o n s tan t space k. space T h e space b l o c k space o f space m a s s space m subscript 2 space i s space g i v e n space a space s h a r p space i m p u l s e space s o space t h a t space i t space a c q u i r e s space a space v e l o c i t y space v subscript 0 space t o w a r d space r i g h t. space I f space s p r i n g space b r e a k space w h e n space v e l o c i t y space o f space m subscript 2 space i s space fraction numerator 3 v subscript 0 over denominator 4 end fraction space t h e space v e l o c i t y space o f space o t h e r space b l o c k space w i l l space b e space$

PhysicsMechanics

$text Two blocks of masses m end text subscript text 1 end text end subscript text and m end text subscript text 2 end text end subscript text are connected by a spring of spring constant k. end text text The block of mass m end text subscript text 2 end text end subscript text is given a sharp impulse so that it acquires a velocity v end text subscript text 0 end text end subscript text toward right end text text Find maximum elongation of spring end text$

$text Two blocks of masses m end text subscript text 1 end text end subscript text and m end text subscript text 2 end text end subscript text are connected by a spring of spring constant k. end text text The block of mass m end text subscript text 2 end text end subscript text is given a sharp impulse so that it acquires a velocity v end text subscript text 0 end text end subscript text toward right end text text Find maximum elongation of spring end text$

PhysicsMechanics

$1. T w o space b l o c k s space o f space m a s s e s space m subscript 1 space a n d space m subscript 2 space a r e space space c o n n e c t e d space b y space a space s p r i n g space o f space s p r i n g space c o n s tan t space k. space T h e space b l o c k space o f space m a s s space m subscript 2 space i s space g i v e n space a space s h a r p space i m p u l s e space s o space t h a t space i t space a c q u i r e s space a space v e l o c i t y space v subscript 0 space t o w a r d space r i g h t. space space space V e l o c i t y space o f space c e n t r e space o f space m a s s space w i l l space b e space space$

$1. T w o space b l o c k s space o f space m a s s e s space m subscript 1 space a n d space m subscript 2 space a r e space space c o n n e c t e d space b y space a space s p r i n g space o f space s p r i n g space c o n s tan t space k. space T h e space b l o c k space o f space m a s s space m subscript 2 space i s space g i v e n space a space s h a r p space i m p u l s e space s o space t h a t space i t space a c q u i r e s space a space v e l o c i t y space v subscript 0 space t o w a r d space r i g h t. space space space V e l o c i t y space o f space c e n t r e space o f space m a s s space w i l l space b e space space$

PhysicsMechanics

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A projectile is fixed with velocity v₀ = 2m/s at angle 60º with horizontal. At top of its trajectory it explodes into three fragment of equal mass. First fragment retraces the path, second moves vertically upward with speed $fraction numerator 3 straight V subscript 0 over denominator 2 end fraction$ . The speed of third fragment (in m/s) is –

A projectile is fixed with velocity v₀ = 2m/s at angle 60º with horizontal. At top of its trajectory it explodes into three fragment of equal mass. First fragment retraces the path, second moves vertically upward with speed $fraction numerator 3 straight V subscript 0 over denominator 2 end fraction$ . The speed of third fragment (in m/s) is –

PhysicsMechanics

A steel ball of radius R = 20 cm and m = 2 kg is rotating about a horizontal diameter with angular speed w₀ = 50 rad/sec. This rotating ball is dropped on a rough horizontal floor and fall freely through a height h = 1.25 m. The coefficient of restitution is e = 1 and coefficient of friction between ball and floor is $mu equals 0.3$ . Then the distance in m between the point of first and second impact of the ball and floor is

A steel ball of radius R = 20 cm and m = 2 kg is rotating about a horizontal diameter with angular speed w₀ = 50 rad/sec. This rotating ball is dropped on a rough horizontal floor and fall freely through a height h = 1.25 m. The coefficient of restitution is e = 1 and coefficient of friction between ball and floor is $mu equals 0.3$ . Then the distance in m between the point of first and second impact of the ball and floor is

PhysicsMechanics

Three identical balls each of mass m = 0.5 kg are connected with ideal string as shown in figure and this system rests on a smooth horizontal table. At moment t = 0 ball B is imparted a velocity v₀ = 9 m/s as shown. Then the velocity of A in m/s when it collides with ball C.

Three identical balls each of mass m = 0.5 kg are connected with ideal string as shown in figure and this system rests on a smooth horizontal table. At moment t = 0 ball B is imparted a velocity v₀ = 9 m/s as shown. Then the velocity of A in m/s when it collides with ball C.

PhysicsMechanics

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