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Physics

Mechanics

Easy

Question

Two particles each of mass m are placed at A and C as such AB = BC = L. The gravitational force on the third particle placed at D at a distance L metre on the perpendicular bisector of the line AC, is –

$\frac{{Gm}^{2}}{\sqrt{2 L^{2}}} along BD$
$\frac{{Gm}^{2}}{\sqrt{2} L^{2}} along DB$
$\frac{{Gm}^{2}}{L^{2}} along AC$
None of these

The correct answer is: $fraction numerator Gm squared over denominator square root of 2 straight L squared end fraction text along end text DB$

$text Angle end text straight angle ADC equals 90 to the power of ring operator table attributes columnalign right left right left right left right left right left right left columnspacing 0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em rowspacing 3 pt end attributes row cell not stretchy rightwards double arrow text distance end text AC equals DC equals square root of 2 lambda end cell row cell not stretchy rightwards double arrow straight F subscript AB perpendicular straight F subscript CD end cell end table$

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A spherical hole is made in a solid sphere of radius R. The mass of the sphere before hollowing was M. The gravitational field at the centre of the hole due to the remaining mass is

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$text The gravitational field in a region is end text 10 straight N divided by kg left parenthesis i with not stretchy hat on top minus j with not stretchy hat on top right parenthesis. text The work done by end text g r a v i t a t i o n a l space f o r c e space t o space s h i f t space s l o w l y space a space p a r t i c l e space o f space m a s s space 1 space k g space f r o m space p o i n t space left parenthesis 1 m comma space 1 m right parenthesis space t o space a space p o i n t space left parenthesis 2 m comma space minus 2 m right parenthesis space i s space space space space space$

$text The gravitational field in a region is end text 10 straight N divided by kg left parenthesis i with not stretchy hat on top minus j with not stretchy hat on top right parenthesis. text The work done by end text g r a v i t a t i o n a l space f o r c e space t o space s h i f t space s l o w l y space a space p a r t i c l e space o f space m a s s space 1 space k g space f r o m space p o i n t space left parenthesis 1 m comma space 1 m right parenthesis space t o space a space p o i n t space left parenthesis 2 m comma space minus 2 m right parenthesis space i s space space space space space$

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There are two bodies of masses 100 kg and 10000 kg separated by a distance 1 m. At what distance from the smaller body, the intensity of gravitational field will be zero?

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A spherical hole is made in a solid sphere of radius R. The mass of the sphere before hollowing was M. The gravitational field at the centre of the hole due to the remaining mass is –

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A mass m is placed in the cavity inside a uniform hollow sphere of mass M as shown in the figure. What is the gravitational force on the mass m?

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$T w o space l e a d space s p h e r e s space o f space s a m e space r a d i u s space a r e space i n space c o n t a c t space w i t h space e a c h space o t h e r. space T h e space g r a v i t a t i o n a l space f o r c e space o f space a t t r a c t i o n space b e t w e e n space t h e m space i s space F. space I f space t w o space l e a d space s p h e r e s space o f space d o u b l e space t h e space p r e v i o u s space r a d i u s space a r e space i n space c o n t a c t space w i t h space e a c h space o t h e r comma space t h e space g r a v i t a t i o n a l space f o r c e space o f space a t t r a c t i o n space b e t w e e n space t h e m space w i l l space b e$

$T w o space l e a d space s p h e r e s space o f space s a m e space r a d i u s space a r e space i n space c o n t a c t space w i t h space e a c h space o t h e r. space T h e space g r a v i t a t i o n a l space f o r c e space o f space a t t r a c t i o n space b e t w e e n space t h e m space i s space F. space I f space t w o space l e a d space s p h e r e s space o f space d o u b l e space t h e space p r e v i o u s space r a d i u s space a r e space i n space c o n t a c t space w i t h space e a c h space o t h e r comma space t h e space g r a v i t a t i o n a l space f o r c e space o f space a t t r a c t i o n space b e t w e e n space t h e m space w i l l space b e$

PhysicsMechanics

$T w o space m e t a l space s p h e r e s space e a c h space o f space r a d i u s space ‘ r ’ space a r e space k e p t space i n space c o n t a c t space w i t h space e a c h space o t h e r. space I f space d space i s space t h e space d e n s i t y space o f space t h e space m a t e r i a l space o f space t h e space s p h e r e comma space t h e n space t h e space g r a v i t a t i o n a l space f o r c e space b e t w e e n space t h o s e space s p h e r e s space i s space p r o p o r t i o n a l space t o$

$T w o space m e t a l space s p h e r e s space e a c h space o f space r a d i u s space ‘ r ’ space a r e space k e p t space i n space c o n t a c t space w i t h space e a c h space o t h e r. space I f space d space i s space t h e space d e n s i t y space o f space t h e space m a t e r i a l space o f space t h e space s p h e r e comma space t h e n space t h e space g r a v i t a t i o n a l space f o r c e space b e t w e e n space t h o s e space s p h e r e s space i s space p r o p o r t i o n a l space t o$

PhysicsMechanics

$T w o space p a r t i c l e s space e a c h space o f space m a s s space ‘ m ’ space a r e space p l a c e d space a t space A space a n d space C space a r e space s u c h space A B equals B C equals L. space T h e space g r a v i t a t i o n a l space f o r c e space o n space t h e space t h i r d space p a r t i c l e space p l a c e d space a t space D space a t space a space d i s tan c e space L space o n space t h e space p e r p e n d i c u l a r space b i s e c t o r space o f space t h e space l i n e space A C space i s$

$T w o space p a r t i c l e s space e a c h space o f space m a s s space ‘ m ’ space a r e space p l a c e d space a t space A space a n d space C space a r e space s u c h space A B equals B C equals L. space T h e space g r a v i t a t i o n a l space f o r c e space o n space t h e space t h i r d space p a r t i c l e space p l a c e d space a t space D space a t space a space d i s tan c e space L space o n space t h e space p e r p e n d i c u l a r space b i s e c t o r space o f space t h e space l i n e space A C space i s$

PhysicsMechanics

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$T h r e e space i d e n t i c a l space p a r t i c l e s space e a c h space o f space m a s s space “ m ” space a r e space a r r a n g e d space a t space t h e space c o r n e r s space o f space a n space e q u i l a t e r a l space t r i a n g l e space o f space s i d e space “ L ”. space I f space t h e y space a r e space t o space b e space i n space e q u i l i b r i u m comma space t h e space s p e e d space w i t h space w h i c h space t h e y space m u s t space r e v o l v e space u n d e r space t h e space i n f l u e n c e space o f space o n e space a n o t h e r ’ s space g r a v i t y space i n space a space c i r c u l a r space o r b i t space c i r c u m s c r i b i n g space t h e space t r i a n g l e space i s$

$T h r e e space i d e n t i c a l space p a r t i c l e s space e a c h space o f space m a s s space “ m ” space a r e space a r r a n g e d space a t space t h e space c o r n e r s space o f space a n space e q u i l a t e r a l space t r i a n g l e space o f space s i d e space “ L ”. space I f space t h e y space a r e space t o space b e space i n space e q u i l i b r i u m comma space t h e space s p e e d space w i t h space w h i c h space t h e y space m u s t space r e v o l v e space u n d e r space t h e space i n f l u e n c e space o f space o n e space a n o t h e r ’ s space g r a v i t y space i n space a space c i r c u l a r space o r b i t space c i r c u m s c r i b i n g space t h e space t r i a n g l e space i s$

PhysicsMechanics

$T w o space l e a d space b a l l s space o f space m a s s e s space m space a n d space 5 m space h a v i n g space r a d i i space R space a n d space 2 R space a r e space s e p a r a t e d space b y space 12 R. space I f space t h e y space a t t r a c t space e a c h space o t h e r space b y space g r a v i t a t i o n a l space f o r c e comma space t h e space d i s tan c e space c o v e r e d space b y space s m a l l space s p h e r e space b e f o r e space t h e y space t o u c h space e a c h space$

$T w o space l e a d space b a l l s space o f space m a s s e s space m space a n d space 5 m space h a v i n g space r a d i i space R space a n d space 2 R space a r e space s e p a r a t e d space b y space 12 R. space I f space t h e y space a t t r a c t space e a c h space o t h e r space b y space g r a v i t a t i o n a l space f o r c e comma space t h e space d i s tan c e space c o v e r e d space b y space s m a l l space s p h e r e space b e f o r e space t h e y space t o u c h space e a c h space$

PhysicsMechanics

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

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

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$I f space t h e space m a s s space o f space o n e space p a r t i c l e space i s space i n c r e a s e d space b y space 50 percent sign space a n d space t h e space m a s s space o f space a n o t h e r space p a r t i c l e space i s space d e c r e a s e d space b y space 50 space percent sign comma space t h e space f o r c e space b e t w e e n space t h e m$

$I f space t h e space m a s s space o f space o n e space p a r t i c l e space i s space i n c r e a s e d space b y space 50 percent sign space a n d space t h e space m a s s space o f space a n o t h e r space p a r t i c l e space i s space d e c r e a s e d space b y space 50 space percent sign comma space t h e space f o r c e space b e t w e e n space t h e m$

PhysicsMechanics

$T w o space m a s s e s space ‘ M ’ space a n d space ‘ 4 M ’ space a r e space a t space a space d i s tan c e space ‘ r ’ space a p a r t space o n space t h e space l i n e space j o i n i n g space t h e m comma space ‘ P ’ space i s p o i n t space w h e r e space t h e space r e s u l tan t space g r a v i t a t i o n a l space f o r c e space i s space z e r o space left parenthesis s u c h space a space p o i n t space i s space c a l l e d space a s space n u l l space p o i n t right parenthesis. space T h e space d i s tan c e space o f space ‘ P ’ space f r o m space t h e space m a s s space ‘ M ’ space i s$

$T w o space m a s s e s space ‘ M ’ space a n d space ‘ 4 M ’ space a r e space a t space a space d i s tan c e space ‘ r ’ space a p a r t space o n space t h e space l i n e space j o i n i n g space t h e m comma space ‘ P ’ space i s p o i n t space w h e r e space t h e space r e s u l tan t space g r a v i t a t i o n a l space f o r c e space i s space z e r o space left parenthesis s u c h space a space p o i n t space i s space c a l l e d space a s space n u l l space p o i n t right parenthesis. space T h e space d i s tan c e space o f space ‘ P ’ space f r o m space t h e space m a s s space ‘ M ’ space i s$

PhysicsMechanics

$I f space t h r e e space p a r t i c l e s comma space e a c h space o f space m a s s space M space a r e space p l a c e d space a t space t h e space t h r e e space c o r n e r s space o f space a n space e q u i l a t e r a l space t r i a n g l e space o f space s i d e space a comma space t h e space f o r c e space e x e r t e d space b y space t h i s space s y s t e m space o n space a n o t h e r space p a r t i c l e space o f space m a s s space M space p l a c e d space left parenthesis i right parenthesis space a t space t h e space m i d p o i n t space o f space a space s i d e space a n d space left parenthesis i i right parenthesis space a t space t h e space c e n t r e space o f space t h e space t r i a n g l e space a r e comma space r e s p e c t i v e l y.$

$I f space t h r e e space p a r t i c l e s comma space e a c h space o f space m a s s space M space a r e space p l a c e d space a t space t h e space t h r e e space c o r n e r s space o f space a n space e q u i l a t e r a l space t r i a n g l e space o f space s i d e space a comma space t h e space f o r c e space e x e r t e d space b y space t h i s space s y s t e m space o n space a n o t h e r space p a r t i c l e space o f space m a s s space M space p l a c e d space left parenthesis i right parenthesis space a t space t h e space m i d p o i n t space o f space a space s i d e space a n d space left parenthesis i i right parenthesis space a t space t h e space c e n t r e space o f space t h e space t r i a n g l e space a r e comma space r e s p e c t i v e l y.$

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