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

Three particles of masses $1 kg comma 3 over 2 kg$ , and 2 kg are located the vertices of an equilateral triangle of side a. The x, y coordinates of the centre of mass are

$(\frac{5 a}{9}, \frac{2 a}{3 \sqrt{3}})$
$(\frac{2 a}{33}, \frac{5 a}{9})$
$(\frac{5 a}{9}, \frac{2 a}{\sqrt{3}})$
$(\frac{2 a}{\sqrt{3}}, \frac{5 a}{9})$

The correct answer is: $open parentheses fraction numerator 5 a over denominator 9 end fraction comma fraction numerator 2 a over denominator 3 square root of 3 end fraction close parentheses$

Related Questions to study

A small body slides down a smooth uneven surface from a height H, which eventually emerges into a circular loop of radius R(<H) what should be the value of H, so the that force on the body at A is $square root of 2$ times its weight?

A small body slides down a smooth uneven surface from a height H, which eventually emerges into a circular loop of radius R(<H) what should be the value of H, so the that force on the body at A is $square root of 2$ times its weight?

PhysicsMechanics

A ball whirls around in a vertical circle at the end of a string. The other end of the string is fixed at the center of the circle. Assuming the total energy of the ball-Earth system remains constant. What is the difference of tension in string at bottom and top during circular motion $open parentheses T subscript text bolem end text end subscript minus T subscript text sop end text end subscript equals ? close parentheses$

A ball whirls around in a vertical circle at the end of a string. The other end of the string is fixed at the center of the circle. Assuming the total energy of the ball-Earth system remains constant. What is the difference of tension in string at bottom and top during circular motion $open parentheses T subscript text bolem end text end subscript minus T subscript text sop end text end subscript equals ? close parentheses$

PhysicsMechanics

A particle moves from rest at A on the surface of a smooth circular cylinder of radius r as shown. At B it leaves the cylinder. The equation relating $alpha text and end text beta$ is

A particle moves from rest at A on the surface of a smooth circular cylinder of radius r as shown. At B it leaves the cylinder. The equation relating $alpha text and end text beta$ is

PhysicsMechanics

parallel

Three identical particles each of mass 1kg are placed with their centres on a straight line. Their centres are marked A,B and C respectively. The distance of centre of mass of the system from A is

Three identical particles each of mass 1kg are placed with their centres on a straight line. Their centres are marked A,B and C respectively. The distance of centre of mass of the system from A is

PhysicsMechanics

A weightless rod of length 2l carries two equal masses ‘m’, one tied at lower end A and the other at the middle of the rod at B. The rod can rotate in vertical plane about a fixed horizontal axis passing through C. The rod is released from rest in horizontal position. The speed of the mass B at the instant rod, become vertical is:

A weightless rod of length 2l carries two equal masses ‘m’, one tied at lower end A and the other at the middle of the rod at B. The rod can rotate in vertical plane about a fixed horizontal axis passing through C. The rod is released from rest in horizontal position. The speed of the mass B at the instant rod, become vertical is:

PhysicsMechanics

$A space m a n space left parenthesis m a s s space equals 50 space k g right parenthesis space a n d space h i s space s o n space left parenthesis m a s s space equals 20 space k g right parenthesis space a r e space s tan d i n g space o n space a space f r i c t i o n l e s s space s u r f a c e space f a c i n g space e a c h space o t h e r. space T h e space m a n space p u s h e s space h i s space s o n space s o space t h a t space h e space s t a r t s space m o v i n g space a t space a space s p e e d space o f space 0.70 space m s to the power of negative 1 end exponent space w i t h space r e s p e c t space t o space t h e space m a n. space T h e space s p e e d space o f space t h e space m a n space w i t h space r e s p e c t space t o space t h e space s u r f a c e space i s space colon$

$A space m a n space left parenthesis m a s s space equals 50 space k g right parenthesis space a n d space h i s space s o n space left parenthesis m a s s space equals 20 space k g right parenthesis space a r e space s tan d i n g space o n space a space f r i c t i o n l e s s space s u r f a c e space f a c i n g space e a c h space o t h e r. space T h e space m a n space p u s h e s space h i s space s o n space s o space t h a t space h e space s t a r t s space m o v i n g space a t space a space s p e e d space o f space 0.70 space m s to the power of negative 1 end exponent space w i t h space r e s p e c t space t o space t h e space m a n. space T h e space s p e e d space o f space t h e space m a n space w i t h space r e s p e c t space t o space t h e space s u r f a c e space i s space colon$

PhysicsMechanics

parallel

$T h e space t r a j e c t o r y space o f space a space p r o j e c t i l e space n e a r space t h e space s u r f a c e space o f space t h e space e a r t h space i s space g i v e n space a s space y equals 2 space x minus 9 space x squared. space I f space i t space w e r e space l a u n c h e d space a t space a n space a n g l e space theta subscript 0 space w i t h space s p e e d space v subscript 0 space t h e n space left parenthesis g equals 10 space m space s to the power of negative 2 end exponent right parenthesis colon$

$T h e space t r a j e c t o r y space o f space a space p r o j e c t i l e space n e a r space t h e space s u r f a c e space o f space t h e space e a r t h space i s space g i v e n space a s space y equals 2 space x minus 9 space x squared. space I f space i t space w e r e space l a u n c h e d space a t space a n space a n g l e space theta subscript 0 space w i t h space s p e e d space v subscript 0 space t h e n space left parenthesis g equals 10 space m space s to the power of negative 2 end exponent right parenthesis colon$

PhysicsMechanics

$A space u n i f o r m space r o d space o f space l e n g t h space ell space space i s space b e i n g space r o t a t e d space i n space a space h o r i z o n t a l space p l a n e space w i t h space a space c o n s tan t space a n g u l a r space s p e e d space a b o u t space a n space a x i s space p a s sin g space t h r o u g h space o n e space o f space i t s space e n d s. space I f space t h e space t e n s i o n space g e n e r a t e d space i n space t h e space r o d space d u e space t o space r o t a t i o n space i s space T left parenthesis x right parenthesis space a t space a space d i s tan c e space x space f r o m space t h e space a x i s comma space t h e n space w h i c h space o f space t h e space f o l l o w i n g space g r a p h s space d e p i c t s space i t space m o s t space c l o s e l y ?$

$A space u n i f o r m space r o d space o f space l e n g t h space ell space space i s space b e i n g space r o t a t e d space i n space a space h o r i z o n t a l space p l a n e space w i t h space a space c o n s tan t space a n g u l a r space s p e e d space a b o u t space a n space a x i s space p a s sin g space t h r o u g h space o n e space o f space i t s space e n d s. space I f space t h e space t e n s i o n space g e n e r a t e d space i n space t h e space r o d space d u e space t o space r o t a t i o n space i s space T left parenthesis x right parenthesis space a t space a space d i s tan c e space x space f r o m space t h e space a x i s comma space t h e n space w h i c h space o f space t h e space f o l l o w i n g space g r a p h s space d e p i c t s space i t space m o s t space c l o s e l y ?$

PhysicsMechanics

$A space c i r c u l a r space d i s c space o f space r a d i u s space b space h a s space a space h o l e space o f space r a d i u s space a space a t space i t s space c e n t r e space left parenthesis s e e space f i g u r e right parenthesis. space I f space t h e space m a s s space p e r space u n i t space a r e a space o f space t h e space d i s c space v a r i e s space a s space open parentheses sigma subscript 0 over r close parentheses comma space t h e n space t h e space r a d i u s space o f space g y r a t i o n space o f space t h e space d i s c space a b o u t space i t s space a x i s space p a s sin g space t h r o u g h space t h e space c e n t r e space i s colon$

$A space c i r c u l a r space d i s c space o f space r a d i u s space b space h a s space a space h o l e space o f space r a d i u s space a space a t space i t s space c e n t r e space left parenthesis s e e space f i g u r e right parenthesis. space I f space t h e space m a s s space p e r space u n i t space a r e a space o f space t h e space d i s c space v a r i e s space a s space open parentheses sigma subscript 0 over r close parentheses comma space t h e n space t h e space r a d i u s space o f space g y r a t i o n space o f space t h e space d i s c space a b o u t space i t s space a x i s space p a s sin g space t h r o u g h space t h e space c e n t r e space i s colon$

PhysicsMechanics

parallel

$A space s h e l l space i s space f i r e d space f r o m space a space f i x e d space a r t i l l e r y space g u n space w i t h space a n space i n i t i a l space s p e e d space u space s u c h space t h a t space i t space h i t s space t h e space t a r g e t space o n space t h e space g r o u n d space a t space a space d i s tan c e space R space f r o m space i t. space I f space t subscript 1 space a n d space t subscript 2 space a r e space t h e space v a l u e s space o f space t h e space t i m e space t a k e n space b y space i t space t o space h i t space t h e space t a r g e t space i n space t w o space p o s s i b l e space w a y s comma space t h e space p r o d u c t space t subscript 1 space t subscript 2 space i s space equals$

$A space s h e l l space i s space f i r e d space f r o m space a space f i x e d space a r t i l l e r y space g u n space w i t h space a n space i n i t i a l space s p e e d space u space s u c h space t h a t space i t space h i t s space t h e space t a r g e t space o n space t h e space g r o u n d space a t space a space d i s tan c e space R space f r o m space i t. space I f space t subscript 1 space a n d space t subscript 2 space a r e space t h e space v a l u e s space o f space t h e space t i m e space t a k e n space b y space i t space t o space h i t space t h e space t a r g e t space i n space t w o space p o s s i b l e space w a y s comma space t h e space p r o d u c t space t subscript 1 space t subscript 2 space i s space equals$

PhysicsMechanics

$A space p l a n e space i s space i n c l i n e d space a t space a n space a n g l e space alpha equals 30 degree space w i t h space r e s p e c t space t o space t h e space h o r i z o n t a l. space A space p a r t i c l e space i s space p r o j e c t e d space w i t h space a space s p e e d space u equals space 2 space m s space to the power of negative 1 end exponent comma space f r o m space t h e space b a s e space o f space t h e space p l a n e comma space m a k i n g space a n space a n g l e space theta equals 15 degree space w i t h space r e s p e c t space t o space t h e space p l a n e space a s space s h o w n space i n space t h e space f i g u r e. space t h e space d i s tan c e space f r o m space t h e space b a s e comma space a t space w h i c h space t h e space p a r t i c l e space h i t s space t h e space p l a n e space i s space c l o s e space t o space colon space left parenthesis T a k e space g equals 10 m s to the power of negative 2 end exponent right parenthesis$

$A space p l a n e space i s space i n c l i n e d space a t space a n space a n g l e space alpha equals 30 degree space w i t h space r e s p e c t space t o space t h e space h o r i z o n t a l. space A space p a r t i c l e space i s space p r o j e c t e d space w i t h space a space s p e e d space u equals space 2 space m s space to the power of negative 1 end exponent comma space f r o m space t h e space b a s e space o f space t h e space p l a n e comma space m a k i n g space a n space a n g l e space theta equals 15 degree space w i t h space r e s p e c t space t o space t h e space p l a n e space a s space s h o w n space i n space t h e space f i g u r e. space t h e space d i s tan c e space f r o m space t h e space b a s e comma space a t space w h i c h space t h e space p a r t i c l e space h i t s space t h e space p l a n e space i s space c l o s e space t o space colon space left parenthesis T a k e space g equals 10 m s to the power of negative 2 end exponent right parenthesis$

PhysicsMechanics

$T h e space t i m e space d e p e n d e n c e space o f space t h e space p o s i t i o n space o f space a space p a r t i c l e space o f space m a s s space m equals 2 space i s space g i v e n space b y space r with rightwards arrow on top left parenthesis t right parenthesis equals 2 t i with hat on top minus 3 t squared j with hat on top. space I t s space a n g u l a r space m o m e n t u m comma space w i t h space r e s p e c t space t o space t h e space o r i g i n comma space a t space t i m e space t equals 2 space i s$

$T h e space t i m e space d e p e n d e n c e space o f space t h e space p o s i t i o n space o f space a space p a r t i c l e space o f space m a s s space m equals 2 space i s space g i v e n space b y space r with rightwards arrow on top left parenthesis t right parenthesis equals 2 t i with hat on top minus 3 t squared j with hat on top. space I t s space a n g u l a r space m o m e n t u m comma space w i t h space r e s p e c t space t o space t h e space o r i g i n comma space a t space t i m e space t equals 2 space i s$

PhysicsMechanics

parallel

$A space s o l i d space s p h e r e space o f space m a s s space M space a n d space r a d i u s space R space i s space d i v i d e d space i n t o space t w o space u n e q u a l space p a r t s. space T h e space f i r s t space p a r t space h a s space a space m a s s space o f space fraction numerator 7 M over denominator 8 end fraction space a n d space i s space c o n v e r t e d space i n t o space a space u n i f o r m space d i s c space o f space r a d i u s space 2 space R. space T h e space s e c o n d space p a r t space i s space c o n v e r t e d space i n t o space a space u n i f o r m space s o l i d space s p h e r e. space L e t space I subscript 1 space b e space t h e space m o m e n t space o f space i n e r t i a space o f space t h e space d i s c space a b o u t space i t s space a x i s space a n d space I subscript 2 space b e space t h e space m o m e n t space o f space i n e r t i a space o f space t h e space n e w space s p h e r e space a b o u t space i t s space a x i s. space T h e space r a t i o space I subscript 1 space divided by space I subscript 2 space i s space g i v e n space b y colon$

$A space s o l i d space s p h e r e space o f space m a s s space M space a n d space r a d i u s space R space i s space d i v i d e d space i n t o space t w o space u n e q u a l space p a r t s. space T h e space f i r s t space p a r t space h a s space a space m a s s space o f space fraction numerator 7 M over denominator 8 end fraction space a n d space i s space c o n v e r t e d space i n t o space a space u n i f o r m space d i s c space o f space r a d i u s space 2 space R. space T h e space s e c o n d space p a r t space i s space c o n v e r t e d space i n t o space a space u n i f o r m space s o l i d space s p h e r e. space L e t space I subscript 1 space b e space t h e space m o m e n t space o f space i n e r t i a space o f space t h e space d i s c space a b o u t space i t s space a x i s space a n d space I subscript 2 space b e space t h e space m o m e n t space o f space i n e r t i a space o f space t h e space n e w space s p h e r e space a b o u t space i t s space a x i s. space T h e space r a t i o space I subscript 1 space divided by space I subscript 2 space i s space g i v e n space b y colon$

PhysicsMechanics

$A space m e t a l space c o i n space o f space m a s s space 5 space g space a n d space r a d i u s space 1 space c m space i s space f i x e d space t o space a space t h i n space s t i c k space A B space o f space n e g l i g i b l e space m a s s space a s space s h o w n space i n space t h e space f i g u r e. space T h e space s y s t e m space i s space i n i t i a l l y space a t space r e s t. space T h e space c o n s tan t space t o r q u e comma space t h a t space w i l l space m a k e space t h e space s y s t e m space r o t a t e space a b o u t space A B a t space 25 space r o t a t i o n s space p e r space s e c o n d space i n space 5 space s comma space i s space c l o s e space t o space colon$

$A space m e t a l space c o i n space o f space m a s s space 5 space g space a n d space r a d i u s space 1 space c m space i s space f i x e d space t o space a space t h i n space s t i c k space A B space o f space n e g l i g i b l e space m a s s space a s space s h o w n space i n space t h e space f i g u r e. space T h e space s y s t e m space i s space i n i t i a l l y space a t space r e s t. space T h e space c o n s tan t space t o r q u e comma space t h a t space w i l l space m a k e space t h e space s y s t e m space r o t a t e space a b o u t space A B a t space 25 space r o t a t i o n s space p e r space s e c o n d space i n space 5 space s comma space i s space c l o s e space t o space colon$

PhysicsMechanics

$T w o space c o a x i a l space d i s c s comma space h a v i n g space m o m e n t s space o f space i n e r t i a space space space straight I subscript 1 text and end text straight I subscript 1 over 2 space comma space a r e space r o t a t i n g space w i t h space r e s p e c t i v e space a n g u l a r space v e l o c i t i e s space omega subscript 1 a n d space omega subscript 1 over 2 space comma space a b o u t space t h e i r space c o m m o n space a x i s. space T h e y space a r e space b r o u g h t space i n space c o n t a c t space w i t h space e a c h space o t h e r space a n d space t h e r e a f t e r space t h e y space r o t a t e space w i t h space a space c o m m o n space a n g u l a r space v e l o c i t y. space I f space straight E subscript straight f space space a n d space E subscript i space a r e space t h e space f i n a l space a n d space i n i t i a l space t o t a l space e n e r g i e s comma space t h e n space left parenthesis straight E subscript straight f space – E subscript i right parenthesis space i s space colon space$

$T w o space c o a x i a l space d i s c s comma space h a v i n g space m o m e n t s space o f space i n e r t i a space space space straight I subscript 1 text and end text straight I subscript 1 over 2 space comma space a r e space r o t a t i n g space w i t h space r e s p e c t i v e space a n g u l a r space v e l o c i t i e s space omega subscript 1 a n d space omega subscript 1 over 2 space comma space a b o u t space t h e i r space c o m m o n space a x i s. space T h e y space a r e space b r o u g h t space i n space c o n t a c t space w i t h space e a c h space o t h e r space a n d space t h e r e a f t e r space t h e y space r o t a t e space w i t h space a space c o m m o n space a n g u l a r space v e l o c i t y. space I f space straight E subscript straight f space space a n d space E subscript i space a r e space t h e space f i n a l space a n d space i n i t i a l space t o t a l space e n e r g i e s comma space t h e n space left parenthesis straight E subscript straight f space – E subscript i right parenthesis space i s space colon space$

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.