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Page 1 Q u e s t i o n 1 T h e s t o p p i n g p o t e n t i a l ( V 0 ) v e r s u s f r e q u e n c y ( v ) o f a g r a p h f o r p h o t o e l e c t r i c e f f e c t i n a m e t a l . F r o m t h e g r a p h , t h e p l a n c k ' s c o n s t a n t ( h ) i s . O p t i o n s : A . 6 . 6 0 × 1 0 - 3 4 J - s B . 6 . 6 9 × 1 0 - 3 4 J - s C . 6 . 6 2 × 1 0 - 3 4 J - s D . 6 . 6 3 × 1 0 - 3 4 J - s A n s w e r : A S o l u t i o n : S o l u t i o n : - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Q u e s t i o n 2 I n a r e s o n a n c e c o l u m n f i r s t a n d s e c o n d r e s o n a n c e a r e o b t a i n e d a t d e p t h s 2 4 c m a n d 7 8 c m t h e t h i r d r e s o n a n c e w i l l b e o b t a i n e d a t d e p t h . O p t i o n s : e V 0 = h ( v - v 0 ) = h v - h v 0 V 0 = h e v - h v v 0 . . . . . . . . . . . . . . . . ( i ) F r o m E q . ( i ) , i t f o l l o w s t h a t t h e s l o p e o f t h e g r a p h i s h e . T h e r e f o r e , h = e × s l o p e = 1 . 6 × 1 0 - 1 9 × 1 6 5 - 0 ( 8 - 4 ) × 1 0 1 5 = 1 6 × 1 0 - 1 9 × 1 6 . 5 4 × 1 0 1 5 = 6 . 6 × 1 0 - 3 4 J - s . ( ) ( ) BITSAT - Paper 2022 Solved Paper Page 2 Q u e s t i o n 1 T h e s t o p p i n g p o t e n t i a l ( V 0 ) v e r s u s f r e q u e n c y ( v ) o f a g r a p h f o r p h o t o e l e c t r i c e f f e c t i n a m e t a l . F r o m t h e g r a p h , t h e p l a n c k ' s c o n s t a n t ( h ) i s . O p t i o n s : A . 6 . 6 0 × 1 0 - 3 4 J - s B . 6 . 6 9 × 1 0 - 3 4 J - s C . 6 . 6 2 × 1 0 - 3 4 J - s D . 6 . 6 3 × 1 0 - 3 4 J - s A n s w e r : A S o l u t i o n : S o l u t i o n : - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Q u e s t i o n 2 I n a r e s o n a n c e c o l u m n f i r s t a n d s e c o n d r e s o n a n c e a r e o b t a i n e d a t d e p t h s 2 4 c m a n d 7 8 c m t h e t h i r d r e s o n a n c e w i l l b e o b t a i n e d a t d e p t h . O p t i o n s : e V 0 = h ( v - v 0 ) = h v - h v 0 V 0 = h e v - h v v 0 . . . . . . . . . . . . . . . . ( i ) F r o m E q . ( i ) , i t f o l l o w s t h a t t h e s l o p e o f t h e g r a p h i s h e . T h e r e f o r e , h = e × s l o p e = 1 . 6 × 1 0 - 1 9 × 1 6 5 - 0 ( 8 - 4 ) × 1 0 1 5 = 1 6 × 1 0 - 1 9 × 1 6 . 5 4 × 1 0 1 5 = 6 . 6 × 1 0 - 3 4 J - s . ( ) ( ) BITSAT - Paper 2022 Solved Paper A . 1 6 0 c m B . 1 3 2 c m C . 1 3 1 c m D . 1 5 2 c m A n s w e r : B S o l u t i o n : S o l u t i o n : - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Q u e s t i o n 3 A s u b m a r i n e A t r a v e l l i n g a t 1 7 m s i s b e i n g c h a s e d a l o n g t h e l i n e o f i t s v e l o c i t y b y a n o t h e r s u b m a r i n e B t r a v e l l i n g a t 3 4 m s . B s e n d s a s o n a r s i g n a l o f 6 0 0 H z t o d e t e c t A a n d r e c e i v e s a r e f l e c t e d s o u n d o f f r e q u e n c y v . T h e o f v i s [ S p e e d o f s o u n d i n w a t e r = 1 5 0 0 m s - 1 ] O p t i o n s : A . 6 1 3 . 7 H z B . 6 1 3 7 H z C . 6 2 H z D . 5 3 9 H z A n s w e r : A S o l u t i o n : S o l u t i o n : G i v e n , f i r s t r e s o n a n c e c o l u m n a t d e o t h , l 1 = 2 4 c m S e c o n d r e s o n a n c e c o l u m n a t d e p t h , l 2 = 7 8 c m T h i r d r e s o n a n c e c o l u m n a t d e p t h , l 3 = ? A s l 1 + x = ? 4 = 2 4 . . . . . . . . . . . . . . . ( i ) l 2 + x = 3 ? 4 = 7 8 . . . . . . . . . . . . . . . . ( i i ) l 3 + x = 5 ? 4 . . . . . . . . . . . . . . . . ( i i i ) F r o m E q s . ( i ) a n d ( i i ) , x = l 2 - 3 l 1 2 = 7 8 - 3 ( 2 4 ) 2 = 3 . . . . . . . . . . . . . . . . . . ( i v ) s u b s t i t u t i n g l 1 a n d x v a l u e , w e g e t l 3 = 5 ( 2 4 ) + 4 ( 3 ) ? l 3 = 1 3 2 c m . G i v e n , v e l o c i t y o f s u b m a r i n e A , v A 1 7 m / s V e l o c i t y o f S u b m a r i n e B , v B = 3 4 m / s S i g n a l s e n t b y s u b m a r i n e B i s d e t e c t e d b y s u b m a r i n e A c a n b e s h o w n a s Page 3 Q u e s t i o n 1 T h e s t o p p i n g p o t e n t i a l ( V 0 ) v e r s u s f r e q u e n c y ( v ) o f a g r a p h f o r p h o t o e l e c t r i c e f f e c t i n a m e t a l . F r o m t h e g r a p h , t h e p l a n c k ' s c o n s t a n t ( h ) i s . O p t i o n s : A . 6 . 6 0 × 1 0 - 3 4 J - s B . 6 . 6 9 × 1 0 - 3 4 J - s C . 6 . 6 2 × 1 0 - 3 4 J - s D . 6 . 6 3 × 1 0 - 3 4 J - s A n s w e r : A S o l u t i o n : S o l u t i o n : - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Q u e s t i o n 2 I n a r e s o n a n c e c o l u m n f i r s t a n d s e c o n d r e s o n a n c e a r e o b t a i n e d a t d e p t h s 2 4 c m a n d 7 8 c m t h e t h i r d r e s o n a n c e w i l l b e o b t a i n e d a t d e p t h . O p t i o n s : e V 0 = h ( v - v 0 ) = h v - h v 0 V 0 = h e v - h v v 0 . . . . . . . . . . . . . . . . ( i ) F r o m E q . ( i ) , i t f o l l o w s t h a t t h e s l o p e o f t h e g r a p h i s h e . T h e r e f o r e , h = e × s l o p e = 1 . 6 × 1 0 - 1 9 × 1 6 5 - 0 ( 8 - 4 ) × 1 0 1 5 = 1 6 × 1 0 - 1 9 × 1 6 . 5 4 × 1 0 1 5 = 6 . 6 × 1 0 - 3 4 J - s . ( ) ( ) BITSAT - Paper 2022 Solved Paper A . 1 6 0 c m B . 1 3 2 c m C . 1 3 1 c m D . 1 5 2 c m A n s w e r : B S o l u t i o n : S o l u t i o n : - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Q u e s t i o n 3 A s u b m a r i n e A t r a v e l l i n g a t 1 7 m s i s b e i n g c h a s e d a l o n g t h e l i n e o f i t s v e l o c i t y b y a n o t h e r s u b m a r i n e B t r a v e l l i n g a t 3 4 m s . B s e n d s a s o n a r s i g n a l o f 6 0 0 H z t o d e t e c t A a n d r e c e i v e s a r e f l e c t e d s o u n d o f f r e q u e n c y v . T h e o f v i s [ S p e e d o f s o u n d i n w a t e r = 1 5 0 0 m s - 1 ] O p t i o n s : A . 6 1 3 . 7 H z B . 6 1 3 7 H z C . 6 2 H z D . 5 3 9 H z A n s w e r : A S o l u t i o n : S o l u t i o n : G i v e n , f i r s t r e s o n a n c e c o l u m n a t d e o t h , l 1 = 2 4 c m S e c o n d r e s o n a n c e c o l u m n a t d e p t h , l 2 = 7 8 c m T h i r d r e s o n a n c e c o l u m n a t d e p t h , l 3 = ? A s l 1 + x = ? 4 = 2 4 . . . . . . . . . . . . . . . ( i ) l 2 + x = 3 ? 4 = 7 8 . . . . . . . . . . . . . . . . ( i i ) l 3 + x = 5 ? 4 . . . . . . . . . . . . . . . . ( i i i ) F r o m E q s . ( i ) a n d ( i i ) , x = l 2 - 3 l 1 2 = 7 8 - 3 ( 2 4 ) 2 = 3 . . . . . . . . . . . . . . . . . . ( i v ) s u b s t i t u t i n g l 1 a n d x v a l u e , w e g e t l 3 = 5 ( 2 4 ) + 4 ( 3 ) ? l 3 = 1 3 2 c m . G i v e n , v e l o c i t y o f s u b m a r i n e A , v A 1 7 m / s V e l o c i t y o f S u b m a r i n e B , v B = 3 4 m / s S i g n a l s e n t b y s u b m a r i n e B i s d e t e c t e d b y s u b m a r i n e A c a n b e s h o w n a s - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Q u e s t i o n 4 T r a n s v e r s e w a v e s o f t h e s a m e f r e q u e n c y a r e g e n e r a t e d i n t w o s t e e l w i r e s A a n d B . T h e d i a m e t e r o f A i s t w i c e t h a t o f B a n d t h e t e n s i o n i n A i s h a l f t h a t i n B . T h e r a t i o o f t h e v e l o c i t i e s o f t h e w a v e s i n A a n d B i s O p t i o n s : A . 1 : 2 B . 1 : v 2 C . 1 : 2 v 2 D . 3 : 2 v 2 A n s w e r : C S o l u t i o n : S o l u t i o n : F r e q u e n c y o f t h e s i g n a l , f 0 = 6 0 0 H z s p e e d o f s o u n d i n w a t e r v s = 1 5 0 0 m s - 1 F r e q u e n c y r e c e i v e d b y s u b m a r i n e A i s f 1 = v S - v A v S - v B f 0 = 1 5 0 0 - 1 7 1 5 0 0 - 3 4 × 6 0 0 h z f 1 = 1 4 8 3 1 4 6 6 × 6 0 0 . . . . . . . . . . . . ( i ) F r e q u e n c y r e c e i v e d b y s u b m a r i n e i s f 2 = v S + v B v s v A f 1 S u b s t i t u t i n g g i v e n v a l u e s a n d f 1 v a l u e f r o m E q . ( i ) , w e g e t f 2 = 1 5 0 0 + 3 4 1 5 0 0 + 1 7 × 1 4 8 3 1 4 6 6 × 6 0 0 f 2 = 1 . 0 1 1 2 × 1 . 0 1 1 5 × 6 0 0 f 2 = 6 1 3 . 7 H z . ( ) [ ] ( ) ( ) [ ] T h e v e l o c i t y i f t r a n s v e r s e w a v e s i s g i v e n b y v = T m w h e r e , T = T e n s i o n a n d m = m a s s p e r u n i t l e n g t h o f t h e w i r e . I f r i s t h e r a d i u s i f t h e w i r e a n d ? i t s d e n s i t y t h e n , m = p r 2 ? ? v = T m = T p r 2 ? ? v A = v T A r A v p ? a n d v B = v T B r B v p ? N o w , v a v B = T A T B . r B r A v v v v Page 4 Q u e s t i o n 1 T h e s t o p p i n g p o t e n t i a l ( V 0 ) v e r s u s f r e q u e n c y ( v ) o f a g r a p h f o r p h o t o e l e c t r i c e f f e c t i n a m e t a l . F r o m t h e g r a p h , t h e p l a n c k ' s c o n s t a n t ( h ) i s . O p t i o n s : A . 6 . 6 0 × 1 0 - 3 4 J - s B . 6 . 6 9 × 1 0 - 3 4 J - s C . 6 . 6 2 × 1 0 - 3 4 J - s D . 6 . 6 3 × 1 0 - 3 4 J - s A n s w e r : A S o l u t i o n : S o l u t i o n : - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Q u e s t i o n 2 I n a r e s o n a n c e c o l u m n f i r s t a n d s e c o n d r e s o n a n c e a r e o b t a i n e d a t d e p t h s 2 4 c m a n d 7 8 c m t h e t h i r d r e s o n a n c e w i l l b e o b t a i n e d a t d e p t h . O p t i o n s : e V 0 = h ( v - v 0 ) = h v - h v 0 V 0 = h e v - h v v 0 . . . . . . . . . . . . . . . . ( i ) F r o m E q . ( i ) , i t f o l l o w s t h a t t h e s l o p e o f t h e g r a p h i s h e . T h e r e f o r e , h = e × s l o p e = 1 . 6 × 1 0 - 1 9 × 1 6 5 - 0 ( 8 - 4 ) × 1 0 1 5 = 1 6 × 1 0 - 1 9 × 1 6 . 5 4 × 1 0 1 5 = 6 . 6 × 1 0 - 3 4 J - s . ( ) ( ) BITSAT - Paper 2022 Solved Paper A . 1 6 0 c m B . 1 3 2 c m C . 1 3 1 c m D . 1 5 2 c m A n s w e r : B S o l u t i o n : S o l u t i o n : - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Q u e s t i o n 3 A s u b m a r i n e A t r a v e l l i n g a t 1 7 m s i s b e i n g c h a s e d a l o n g t h e l i n e o f i t s v e l o c i t y b y a n o t h e r s u b m a r i n e B t r a v e l l i n g a t 3 4 m s . B s e n d s a s o n a r s i g n a l o f 6 0 0 H z t o d e t e c t A a n d r e c e i v e s a r e f l e c t e d s o u n d o f f r e q u e n c y v . T h e o f v i s [ S p e e d o f s o u n d i n w a t e r = 1 5 0 0 m s - 1 ] O p t i o n s : A . 6 1 3 . 7 H z B . 6 1 3 7 H z C . 6 2 H z D . 5 3 9 H z A n s w e r : A S o l u t i o n : S o l u t i o n : G i v e n , f i r s t r e s o n a n c e c o l u m n a t d e o t h , l 1 = 2 4 c m S e c o n d r e s o n a n c e c o l u m n a t d e p t h , l 2 = 7 8 c m T h i r d r e s o n a n c e c o l u m n a t d e p t h , l 3 = ? A s l 1 + x = ? 4 = 2 4 . . . . . . . . . . . . . . . ( i ) l 2 + x = 3 ? 4 = 7 8 . . . . . . . . . . . . . . . . ( i i ) l 3 + x = 5 ? 4 . . . . . . . . . . . . . . . . ( i i i ) F r o m E q s . ( i ) a n d ( i i ) , x = l 2 - 3 l 1 2 = 7 8 - 3 ( 2 4 ) 2 = 3 . . . . . . . . . . . . . . . . . . ( i v ) s u b s t i t u t i n g l 1 a n d x v a l u e , w e g e t l 3 = 5 ( 2 4 ) + 4 ( 3 ) ? l 3 = 1 3 2 c m . G i v e n , v e l o c i t y o f s u b m a r i n e A , v A 1 7 m / s V e l o c i t y o f S u b m a r i n e B , v B = 3 4 m / s S i g n a l s e n t b y s u b m a r i n e B i s d e t e c t e d b y s u b m a r i n e A c a n b e s h o w n a s - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Q u e s t i o n 4 T r a n s v e r s e w a v e s o f t h e s a m e f r e q u e n c y a r e g e n e r a t e d i n t w o s t e e l w i r e s A a n d B . T h e d i a m e t e r o f A i s t w i c e t h a t o f B a n d t h e t e n s i o n i n A i s h a l f t h a t i n B . T h e r a t i o o f t h e v e l o c i t i e s o f t h e w a v e s i n A a n d B i s O p t i o n s : A . 1 : 2 B . 1 : v 2 C . 1 : 2 v 2 D . 3 : 2 v 2 A n s w e r : C S o l u t i o n : S o l u t i o n : F r e q u e n c y o f t h e s i g n a l , f 0 = 6 0 0 H z s p e e d o f s o u n d i n w a t e r v s = 1 5 0 0 m s - 1 F r e q u e n c y r e c e i v e d b y s u b m a r i n e A i s f 1 = v S - v A v S - v B f 0 = 1 5 0 0 - 1 7 1 5 0 0 - 3 4 × 6 0 0 h z f 1 = 1 4 8 3 1 4 6 6 × 6 0 0 . . . . . . . . . . . . ( i ) F r e q u e n c y r e c e i v e d b y s u b m a r i n e i s f 2 = v S + v B v s v A f 1 S u b s t i t u t i n g g i v e n v a l u e s a n d f 1 v a l u e f r o m E q . ( i ) , w e g e t f 2 = 1 5 0 0 + 3 4 1 5 0 0 + 1 7 × 1 4 8 3 1 4 6 6 × 6 0 0 f 2 = 1 . 0 1 1 2 × 1 . 0 1 1 5 × 6 0 0 f 2 = 6 1 3 . 7 H z . ( ) [ ] ( ) ( ) [ ] T h e v e l o c i t y i f t r a n s v e r s e w a v e s i s g i v e n b y v = T m w h e r e , T = T e n s i o n a n d m = m a s s p e r u n i t l e n g t h o f t h e w i r e . I f r i s t h e r a d i u s i f t h e w i r e a n d ? i t s d e n s i t y t h e n , m = p r 2 ? ? v = T m = T p r 2 ? ? v A = v T A r A v p ? a n d v B = v T B r B v p ? N o w , v a v B = T A T B . r B r A v v v v - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Q u e s t i o n 5 I n t h e d i a g r a m s h o w n b e l o w , b o t h t h e s t r i n g s A B a n d C D a r e m a d e o f s a m e m a t e r i a l a n d h a v e s a m e c r o s s - s e c t i o n . T h e p u l l e y s a r e l i g h t a n d f i c t i o n l e s s . I f t h e s p e e d o f w a v e i n s t r i n g A B i s v 1 a n d i n C D i s v 2 , t h e n v 1 v 2 i s O p t i o n s : A . 1 B . v 2 C . 2 D . 1 v 2 A n s w e r : D S o l u t i o n : S o l u t i o n : - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Q u e s t i o n 6 W h a t w i l l b e t h e a c c e l e r a t i o n d u e t o g r a v i t y a t a d e p t h d , w h e r e g i s ? r A = 2 r B a n d T A = 1 2 T B H e n c e , v A v B = 1 2 v 2 L e t t h e s p e e d o f w a v e i n s t r i n g b e v a n d t e n s i o n i n s t r i n g b e T . v ? v T v A B v C D = v T 2 T = 1 v 2 Page 5 Q u e s t i o n 1 T h e s t o p p i n g p o t e n t i a l ( V 0 ) v e r s u s f r e q u e n c y ( v ) o f a g r a p h f o r p h o t o e l e c t r i c e f f e c t i n a m e t a l . F r o m t h e g r a p h , t h e p l a n c k ' s c o n s t a n t ( h ) i s . O p t i o n s : A . 6 . 6 0 × 1 0 - 3 4 J - s B . 6 . 6 9 × 1 0 - 3 4 J - s C . 6 . 6 2 × 1 0 - 3 4 J - s D . 6 . 6 3 × 1 0 - 3 4 J - s A n s w e r : A S o l u t i o n : S o l u t i o n : - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Q u e s t i o n 2 I n a r e s o n a n c e c o l u m n f i r s t a n d s e c o n d r e s o n a n c e a r e o b t a i n e d a t d e p t h s 2 4 c m a n d 7 8 c m t h e t h i r d r e s o n a n c e w i l l b e o b t a i n e d a t d e p t h . O p t i o n s : e V 0 = h ( v - v 0 ) = h v - h v 0 V 0 = h e v - h v v 0 . . . . . . . . . . . . . . . . ( i ) F r o m E q . ( i ) , i t f o l l o w s t h a t t h e s l o p e o f t h e g r a p h i s h e . T h e r e f o r e , h = e × s l o p e = 1 . 6 × 1 0 - 1 9 × 1 6 5 - 0 ( 8 - 4 ) × 1 0 1 5 = 1 6 × 1 0 - 1 9 × 1 6 . 5 4 × 1 0 1 5 = 6 . 6 × 1 0 - 3 4 J - s . ( ) ( ) BITSAT - Paper 2022 Solved Paper A . 1 6 0 c m B . 1 3 2 c m C . 1 3 1 c m D . 1 5 2 c m A n s w e r : B S o l u t i o n : S o l u t i o n : - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Q u e s t i o n 3 A s u b m a r i n e A t r a v e l l i n g a t 1 7 m s i s b e i n g c h a s e d a l o n g t h e l i n e o f i t s v e l o c i t y b y a n o t h e r s u b m a r i n e B t r a v e l l i n g a t 3 4 m s . B s e n d s a s o n a r s i g n a l o f 6 0 0 H z t o d e t e c t A a n d r e c e i v e s a r e f l e c t e d s o u n d o f f r e q u e n c y v . T h e o f v i s [ S p e e d o f s o u n d i n w a t e r = 1 5 0 0 m s - 1 ] O p t i o n s : A . 6 1 3 . 7 H z B . 6 1 3 7 H z C . 6 2 H z D . 5 3 9 H z A n s w e r : A S o l u t i o n : S o l u t i o n : G i v e n , f i r s t r e s o n a n c e c o l u m n a t d e o t h , l 1 = 2 4 c m S e c o n d r e s o n a n c e c o l u m n a t d e p t h , l 2 = 7 8 c m T h i r d r e s o n a n c e c o l u m n a t d e p t h , l 3 = ? A s l 1 + x = ? 4 = 2 4 . . . . . . . . . . . . . . . ( i ) l 2 + x = 3 ? 4 = 7 8 . . . . . . . . . . . . . . . . ( i i ) l 3 + x = 5 ? 4 . . . . . . . . . . . . . . . . ( i i i ) F r o m E q s . ( i ) a n d ( i i ) , x = l 2 - 3 l 1 2 = 7 8 - 3 ( 2 4 ) 2 = 3 . . . . . . . . . . . . . . . . . . ( i v ) s u b s t i t u t i n g l 1 a n d x v a l u e , w e g e t l 3 = 5 ( 2 4 ) + 4 ( 3 ) ? l 3 = 1 3 2 c m . G i v e n , v e l o c i t y o f s u b m a r i n e A , v A 1 7 m / s V e l o c i t y o f S u b m a r i n e B , v B = 3 4 m / s S i g n a l s e n t b y s u b m a r i n e B i s d e t e c t e d b y s u b m a r i n e A c a n b e s h o w n a s - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Q u e s t i o n 4 T r a n s v e r s e w a v e s o f t h e s a m e f r e q u e n c y a r e g e n e r a t e d i n t w o s t e e l w i r e s A a n d B . T h e d i a m e t e r o f A i s t w i c e t h a t o f B a n d t h e t e n s i o n i n A i s h a l f t h a t i n B . T h e r a t i o o f t h e v e l o c i t i e s o f t h e w a v e s i n A a n d B i s O p t i o n s : A . 1 : 2 B . 1 : v 2 C . 1 : 2 v 2 D . 3 : 2 v 2 A n s w e r : C S o l u t i o n : S o l u t i o n : F r e q u e n c y o f t h e s i g n a l , f 0 = 6 0 0 H z s p e e d o f s o u n d i n w a t e r v s = 1 5 0 0 m s - 1 F r e q u e n c y r e c e i v e d b y s u b m a r i n e A i s f 1 = v S - v A v S - v B f 0 = 1 5 0 0 - 1 7 1 5 0 0 - 3 4 × 6 0 0 h z f 1 = 1 4 8 3 1 4 6 6 × 6 0 0 . . . . . . . . . . . . ( i ) F r e q u e n c y r e c e i v e d b y s u b m a r i n e i s f 2 = v S + v B v s v A f 1 S u b s t i t u t i n g g i v e n v a l u e s a n d f 1 v a l u e f r o m E q . ( i ) , w e g e t f 2 = 1 5 0 0 + 3 4 1 5 0 0 + 1 7 × 1 4 8 3 1 4 6 6 × 6 0 0 f 2 = 1 . 0 1 1 2 × 1 . 0 1 1 5 × 6 0 0 f 2 = 6 1 3 . 7 H z . ( ) [ ] ( ) ( ) [ ] T h e v e l o c i t y i f t r a n s v e r s e w a v e s i s g i v e n b y v = T m w h e r e , T = T e n s i o n a n d m = m a s s p e r u n i t l e n g t h o f t h e w i r e . I f r i s t h e r a d i u s i f t h e w i r e a n d ? i t s d e n s i t y t h e n , m = p r 2 ? ? v = T m = T p r 2 ? ? v A = v T A r A v p ? a n d v B = v T B r B v p ? N o w , v a v B = T A T B . r B r A v v v v - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Q u e s t i o n 5 I n t h e d i a g r a m s h o w n b e l o w , b o t h t h e s t r i n g s A B a n d C D a r e m a d e o f s a m e m a t e r i a l a n d h a v e s a m e c r o s s - s e c t i o n . T h e p u l l e y s a r e l i g h t a n d f i c t i o n l e s s . I f t h e s p e e d o f w a v e i n s t r i n g A B i s v 1 a n d i n C D i s v 2 , t h e n v 1 v 2 i s O p t i o n s : A . 1 B . v 2 C . 2 D . 1 v 2 A n s w e r : D S o l u t i o n : S o l u t i o n : - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Q u e s t i o n 6 W h a t w i l l b e t h e a c c e l e r a t i o n d u e t o g r a v i t y a t a d e p t h d , w h e r e g i s ? r A = 2 r B a n d T A = 1 2 T B H e n c e , v A v B = 1 2 v 2 L e t t h e s p e e d o f w a v e i n s t r i n g b e v a n d t e n s i o n i n s t r i n g b e T . v ? v T v A B v C D = v T 2 T = 1 v 2 a c c e l e r a t i o n d u e t o g r a v i t y o n t h e s u r f a c e o f e a r t h ? O p t i o n s : A . g 1 + d R 2 B . g 1 - 2 d R C . g 1 - d R 2 D . g 1 - d R A n s w e r : D S o l u t i o n : S o l u t i o n : - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - Q u e s t i o n 7 A d i r e c t c u r r e n t o f 6 A i s s u p e r i m p o s e d o n a n a l t e r n a t i n g c u r r e n t I = 1 0 s i n ? t f l o w i n g t h r o u g h a w i r e . T h e e f f e c t i v e v a l u e o f t h e r e s u l t i n g c u r r e n t w i l l b e O p t i o n s : A . 5 v 2 B . 5 v 3 C . 9 . 2 7 D . 8 . 3 7 A n s w e r : C S o l u t i o n : S o l u t i o n : [ ] [ ] [ ] [ ] A c c e l e r a t i o n d u e t o g r a v i t y a t t h e s u r f a c e o f e a r t h , g = G M R 2 = 4 3 p ? G R . . . . . . . . . . . . . . . . . ( i ) ? M = 4 3 p R 3 . ? W h e r e , ? = d e n s i t y o f e a r t h . A c c e l e r a t i o n d u e t o g r a v i t y a t d e p t h d f r o m t h e s u r f a c e o f e a r t h , g ' = 4 3 p ? G ( R - d ) . . . . . . . . . . . ( i i ) F r o m E q s . ( i ) a n d ( i i ) , w e g e t g ' = g 1 - d R [ ] [ ] G i v e n , I = 6 + 1 0 s i n ? tRead More
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