physics

mechanics

Easy

Question

$space Two particles of masses space 100 gm text and end text 300 gm space space have at a given time velocities space left parenthesis 10 i with hat on top minus 7 j with hat on top minus 3 k with hat on top right parenthesis text end text text and end text left parenthesis 7 i with hat on top minus 9 j with hat on top plus 6 k with hat on top right parenthesis cms to the power of negative 1 end exponent text respectively. Then velocity of centre of mass of the system in end text cms to the power of negative 1 end exponent text is end text$

$\frac{1}{4} (31 \hat{i} - 15 \hat{j} + 34 \hat{k})$
$\frac{1}{4} (31 \hat{i} - 34 \hat{j} + 1 \hat{5} k)$
$\frac{1}{4} (34 \hat{i} - 31 \hat{j} + 15 \hat{k})$
$\frac{1}{4} (15 \hat{i} - 34 \hat{j} + 31 \hat{k})$

The correct answer is: $\frac{1}{4} (31 \hat{i} - 34 \hat{j} + 1 \hat{5} k)$

$v with rightwards arrow on top subscript c m end subscript equals fraction numerator m subscript 1 v with rightwards arrow on top subscript 1 plus m subscript 2 v with rightwards arrow on top subscript 2 over denominator m subscript 1 plus m subscript 2 end fraction equals fraction numerator 100 left parenthesis 10 i with hat on top minus 7 j with hat on top minus 3 k with hat on top right parenthesis plus 300 left parenthesis 7 i with hat on top minus 9 j with hat on top plus 6 k with hat on top right parenthesis over denominator 100 plus 300 end fraction equals 1 fourth left parenthesis 31 i with hat on top minus 34 j with hat on top plus 15 k with hat on top right parenthesis$

$A space 30 k g space p r o j e c t i l e space m o v i n g space h o r i z o n t a l l y space w i t h space a space v e l o c i t y space v with rightwards arrow on top subscript 0 equals left parenthesis 120 m divided by s right parenthesis i with hat on top space e x p l o d e s space i n t o space t w o space f r a g m e n t s space A space a n d space B space o f space m a s s e s space 12 k g space a n d space 18 k g comma space r e s p e c t i v e l y. space T a k i n g space p o i n t space o f space e x p l o s i o n space a s space o r i g i n space a n d space k n o w l e d g e space t h a t space 3 s space l a t e r space t h e space p o s i t i o n space o f space f r a g m e n t space A space i s space left parenthesis 300 m comma space 24 m comma negative 48 m space right parenthesis comma space d e t e r m i n e space t h e space p o s i t i o n space o f space f r a g m e n t space B space a t space t h e space s a m e space i n s tan t. space$

PhysicsMechanics

Mechanics

Physics

$A space b l o c k space i s space r e l e a s e d space o n space t h e space c o n v e x space s u r f a c e space o f space a space h e m i s p h e r i c a l space w e d g e space a s space s h o w n space i n space f i g u r e. space D e t e r m i n e space t h e space d i s p l a c e m e n t space o f space t h e space w e d g e space w h e n space t h e space b l o c k space r e a c h e s space t h e space a n g u l a r space p o s i t i o n space theta.$

PhysicsMechanics

Mechanics

Physics

$A space r i n g space a n d space a space p a r t i c l e space o f space m a s s e s space 2 m space a n d space m space a r e space k e p t space a s space s h o w n space i n space t h e space f i g u r e comma space s u c h space t h a t space t h e space C M space o f space t h e space c o m b i n a t i o n space l i e s space a t space t h e space o r i g i n. space F i n d space x.$

PhysicsMechanics

Mechanics

Physics

$F i g u r e space s h o w s space a space u n i f o r m space d i s c space o f space r a d i u s space R comma space f r o m space w h i c h space a space h o l e space o f space r a d i u s space R divided by 2 space h a s space b e e n space c u t space o u t space f r o m space l e f t o f space t h e space c e n t r e space a n d space i s space p l a c e d space o n space t h e space r i g h t space o f space t h e space c e n t r e space o f space t h e space d i s c. space F i n d space t h e space C M space o f space t h e space r e s u l t i n g space d i s c.$

$F o u r space p a r t i c l e s space o f space m a s s e s space 1 space k g space comma space 2 space k g space comma space 3 space k g space a n d space 4 space k g space a r e space p l a c e d space a t space t h e space f o u r space v e r t i c e s A space comma space B space comma space C space a n d space D space o f space a space s q u a r e space o f space s i d e space 1 space m. space F i n d space t h e space p o s i t i o n space o f space c e n t r e space o f space m a s s space o f space t h e space p a r t i c l e s.$

$F o u r space p a r t i c l e s space o f space m a s s e s space 1 K g comma space 2 K g comma space 3 K g space a n d space 4 K g space a r e space p l a c e d space a t space t h e space f o u r space c o m e r s space o f space a space s q u a r e space o f space s i d e space 1 m space a s space s h o w n. space I f space 1 space K g space m a s s space i s space t a k e n space a s space t h e space o r i g i n comma space t h e space c o o r d i n a t e s space o f space c e n t r e space o f space m a s s space o f space t h e space s y s t e m space a r e$

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