Have a query? Ask a Tutor!!

Access to best educators and exclusive paper discussions

Offsite Campus Turito Championship

Can’t find what you’re looking for?

Our tutors are from top schools around the world, and they are waiting for you 24/7, anytime, anywhere.

Homework- One to One Solutions
Understand concepts to solve better
Get your doubts solved instantly

Physics

Mechanics

Easy

Question

A point mass is orbiting a significant mass M lying at the focus of the elliptical orbit having major and minor axes given by 2a and 2b respectively. Let r be the distance between the mass M and the end point of major axis. Velocity of the particle can be given as

$\frac{a b}{r} \sqrt{\frac{G M}{a^{3}}}$
$\frac{a b}{r} \sqrt{\frac{G M}{b^{3}}}$
$\frac{a b}{2 r} \sqrt{\frac{G}{r}}$
$\frac{2 a b}{r} \sqrt{{(\frac{a + b}{2})}^{3}}$

The correct answer is: $fraction numerator a b over denominator r end fraction square root of fraction numerator G M over denominator a cubed end fraction end root$

$text Gravitational force end text equals text Centripetal force end text not stretchy rightwards double arrow fraction numerator G M m over denominator r squared end fraction equals fraction numerator m v squared over denominator r end fraction$
$not stretchy rightwards double arrow fraction numerator G M over denominator r squared end fraction equals v squared over r not stretchy rightwards double arrow fraction numerator G M over denominator a squared end fraction equals fraction numerator left parenthesis a omega right parenthesis squared over denominator a end fraction not stretchy rightwards double arrow omega squared equals fraction numerator G M over denominator a cubed end fraction$
Here r is the radius of curvature .From Kepler's law, time period is given by.
$T equals 2 pi square root of fraction numerator a cubed over denominator G M end fraction end root equals fraction numerator 2 pi a b over denominator r v end fraction open parentheses fraction numerator d A over denominator d t end fraction equals fraction numerator v r over denominator 2 end fraction not stretchy rightwards double arrow d t equals T equals fraction numerator 2 d A over denominator 1 straight percent sign end fraction equals fraction numerator 2 over denominator r v end fraction pi a b close parentheses$
$v equals fraction numerator a b over denominator r end fraction square root of fraction numerator G M over denominator a cubed end fraction end root$

Related Questions to study

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

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

PhysicsMechanics

Two spheres of masses m and M are situated in air and the gravitational force between them is F. The space around the masses is now filled with a liquid of specific gravity 3. The gravitational force will now be –

Two spheres of masses m and M are situated in air and the gravitational force between them is F. The space around the masses is now filled with a liquid of specific gravity 3. The gravitational force will now be –

PhysicsMechanics

A point mass m₀ is placed at distance R/3 from the centre of a spherical shell of mass m and radius R. The gravitational force on the point mass m₀ is -

A point mass m₀ is placed at distance R/3 from the centre of a spherical shell of mass m and radius R. The gravitational force on the point mass m₀ is -

PhysicsMechanics

parallel

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 –

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 –

PhysicsMechanics

The magnitude of the gravitational field at distances r₁ & r₂ from the centre of a uniform sphere of radius R & mass M are F₁ & F₂ respectively then

The magnitude of the gravitational field at distances r₁ & r₂ from the centre of a uniform sphere of radius R & mass M are F₁ & F₂ respectively then

PhysicsMechanics

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

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

PhysicsMechanics

parallel

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

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

PhysicsMechanics

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?

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?

PhysicsMechanics

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 –

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 –

PhysicsMechanics

parallel

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?

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?

PhysicsMechanics

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

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

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

parallel

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

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

PhysicsMechanics

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

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

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

parallel

card img

With Turito Academy.

card img

With Turito Foundation.

card img

Get an Expert Advice From Turito.

Turito Academy

card img

With Turito Academy.

Test Prep

card img

With Turito Foundation.