Physics-
General
Easy

Question

Three identical spheres of mass Meach are placed at the corners of an equilateral triangle of side 2m. Taking one of the corner as the origin, the position vector of the centre of mass is

  1. square root of 3 (stack text i end text with hat on top-stack text j end text with hat on top)    
  2. stack fraction numerator text i end text over denominator square root of 3 end fraction with hat on top +stack text j end text with hat on top    
  3. fraction numerator stack text i end text with hat on top text + end text stack text j end text with hat on top over denominator 3 end fraction    
  4. stack text i end text with hat on top plus stack fraction numerator text j end text over denominator square root of 3 end fraction with hat on top    

The correct answer is: stack fraction numerator text i end text over denominator square root of 3 end fraction with hat on top +stack text j end text with hat on top


    The x coordinate of centre of mass is
    stack x with minus on top equals fraction numerator not stretchy sum m subscript i end subscript x subscript i end subscript over denominator not stretchy sum m subscript i end subscript end fraction
    equals fraction numerator m cross times 0 plus m cross times 1 plus m cross times 2 over denominator m plus m plus m end fraction equals 1
    stack y with minus on top equals fraction numerator not stretchy sum m subscript i end subscript y subscript i end subscript over denominator not stretchy sum m subscript i end subscript end fraction
    equals fraction numerator m cross times 0 plus m left parenthesis 2 sin invisible function application 60 degree right parenthesis plus m cross times 0 over denominator m plus m plus m end fraction
    stack y with minus on top equals fraction numerator square root of 3 m over denominator 3 m end fraction equals fraction numerator 1 over denominator square root of 3 end fraction
    Position vector of centre of mass is open parentheses stack i with hat on top plus fraction numerator stack j with hat on top over denominator square root of 3 end fraction close parentheses.

    Related Questions to study

    General
    physics-

    Four bodies of equal mass start moving with same speed are shown in the figure. In which of the following combination the centre of mass will remain at origin?

    Four bodies of equal mass start moving with same speed are shown in the figure. In which of the following combination the centre of mass will remain at origin?

    physics-General
    General
    chemistry-

    From threactions: C(s)+2H2(g)→CH4(g)DH=–Xcal C(g)+4H(g)→CH4(g),DH=–X1Kcal CH4(g)→CH3(g)+H(g)DH=+Y(Kcal) Bond energof C–H bond is-

    From threactions: C(s)+2H2(g)→CH4(g)DH=–Xcal C(g)+4H(g)→CH4(g),DH=–X1Kcal CH4(g)→CH3(g)+H(g)DH=+Y(Kcal) Bond energof C–H bond is-

    chemistry-General
    General
    physics-

    From a circular disc of radius R and mass 9 M, a small disc of radius R/3 is removed from the disc. The moment of inertia of the remaining disc about an axis perpendicular to the plane of the disc and passing through O is

    From a circular disc of radius R and mass 9 M, a small disc of radius R/3 is removed from the disc. The moment of inertia of the remaining disc about an axis perpendicular to the plane of the disc and passing through O is

    physics-General
    parallel
    General
    physics-

    The instantaneous velocity of a point B of the given rod of length 0.5 m is 3 m s to the power of negative 1 end exponent in the represented direction. The angular velocity of the rod for minimum velocity of end A is

    The instantaneous velocity of a point B of the given rod of length 0.5 m is 3 m s to the power of negative 1 end exponent in the represented direction. The angular velocity of the rod for minimum velocity of end A is

    physics-General
    General
    biology

    The backbone of RNA consists of which of the following sugar?

    The backbone of RNA consists of which of the following sugar?

    biologyGeneral
    General
    biology

    Consider the following statements and choose the correct one

    Consider the following statements and choose the correct one

    biologyGeneral
    parallel
    General
    biology

    Identify A to F in the sectional view of a chloroplast showing the different parts

    Identify A to F in the sectional view of a chloroplast showing the different parts

    biologyGeneral
    General
    biology

    Organelle important in spindle formation during nuclear division is

    Organelle important in spindle formation during nuclear division is

    biologyGeneral
    General
    biology

    A widely accepted, improved model of cell membrane is

    A widely accepted, improved model of cell membrane is

    biologyGeneral
    parallel
    General
    biology

    Rough endoplasmic reticulum differs from smooth walled endoplasmic reticulum due to the presence of

    Rough endoplasmic reticulum differs from smooth walled endoplasmic reticulum due to the presence of

    biologyGeneral
    General
    biology

    Middle lamella is present

    Middle lamella is present

    biologyGeneral
    General
    biology

    A are granular structures first observed under electron microscope as dense particles by …B… (1953). Here, A and B refer to

    A are granular structures first observed under electron microscope as dense particles by …B… (1953). Here, A and B refer to

    biologyGeneral
    parallel
    General
    biology

    Number of protofilament in microtubule is

    Number of protofilament in microtubule is

    biologyGeneral
    General
    biology

    Ribosomes that occur exclusively in mitochondria is

    Ribosomes that occur exclusively in mitochondria is

    biologyGeneral
    General
    physics-

    A T shaped object with dimension shown in the figure, is lying on a smooth floor. A force F is applied at the point P parallel to A B, such that the object has only the translational motion without rotation. Find the location of P with respect to C.

    A T shaped object with dimension shown in the figure, is lying on a smooth floor. A force F is applied at the point P parallel to A B, such that the object has only the translational motion without rotation. Find the location of P with respect to C.

    physics-General
    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.