Physics
Mechanics
Easy

Question

From the circular disc of radius 4 R two small disc of radius R are cut off. The centre of mass of the new structure will be:

  1. i with hat on top R over 5 plus j with hat on top R over 5
  2. negative i with hat on top R over 5 plus j with hat on top R over 5
  3. fraction numerator negative 3 R over denominator 14 end fraction left parenthesis i with hat on top plus ȷ with hat on top right parenthesis
  4. None

The correct answer is: fraction numerator negative 3 R over denominator 14 end fraction left parenthesis i with hat on top plus ȷ with hat on top right parenthesis


    Related Questions to study

    Mechanics
    Physics

    Eight solid uniform cubes of edge l are stacked together to form a single cube with centre O. One cube is removed from this system. Distance of the centre of mass of remaining 7 cubes from O is

    Eight solid uniform cubes of edge l are stacked together to form a single cube with centre O. One cube is removed from this system. Distance of the centre of mass of remaining 7 cubes from O is

    PhysicsMechanics
    Mechanics
    Physics

    A wire of uniform cross-section is bent in the shape shown in figure. The co-ordinate of the centre of mass of each side are shown in (figure). The coordinates of the centre of mass of the system are

    A wire of uniform cross-section is bent in the shape shown in figure. The co-ordinate of the centre of mass of each side are shown in (figure). The coordinates of the centre of mass of the system are

    PhysicsMechanics
    Mechanics
    Physics

    Five uniform circular plates, each of diameter b and mass m are laid out in a pattern shown. Using the origin shown. find the y co-ordinate of the centre of mass of the five-plate system.

    Five uniform circular plates, each of diameter b and mass m are laid out in a pattern shown. Using the origin shown. find the y co-ordinate of the centre of mass of the five-plate system.

    PhysicsMechanics
    parallel
    Mechanics
    Physics

    A square of side a and uniform thickness is divided into four equal parts. If upper right part is removed, then find the coordinates of centre of mass of remaining part.

    A square of side a and uniform thickness is divided into four equal parts. If upper right part is removed, then find the coordinates of centre of mass of remaining part.

    PhysicsMechanics
    Mechanics
    Physics

    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

    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

    PhysicsMechanics
    Mechanics
    Physics

    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
    parallel
    Mechanics
    Physics

    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
    Mechanics
    Physics

    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
    Mechanics
    Physics

    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
    parallel
    Mechanics
    Physics

    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
    Mechanics
    Physics

    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
    Mechanics
    Physics

    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
    parallel
    Mechanics
    Physics

    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
    Mechanics
    Physics

    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
    Mechanics
    Physics

    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
    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.