Home
Class 11
PHYSICS
Two balls each of mass 'm' are placed at...

Two balls each of mass 'm' are placed at the vertices A and B of an equilaterial triangle of side 1 m. A third ball of mass 2 m is kept at vertex C. Taking vertex Aas the origin, find the coordinates of the centre-of-mass of the given system.

A

`(1/2m,1/2m)`

B

`(1/2m,sqrt2m)`

C

`(1/2m,sqrt3/4m)`

D

`(sqrt3/4m,sqrt3/4m)`

Text Solution

Verified by Experts

The correct Answer is:
C

Here centre of mass is given by `barx = (m_1x_1 +m_2 x_2+m_3x_3)/(m_1+m_2+m3) , barx = (mxx0 + m xx1 + 2m xx1//2)/(m+m+2m)`
`bar x = (2m)/(4m) =1/2 , bary = (m_1y_1+m_2y_2+m_3y_3)/(m_1+m_2+m_3)`
`bary=(mxx0+mxx0+2mxxsqrt3//2)/(m+m+2m)=sqrt3/4 " " :.` Centre of mass is `[1/2m,sqrt3/4m]`
Doubtnut Promotions Banner Mobile Dark
|

Similar Questions

Explore conceptually related problems

Three particles each of mass m are placed at the comers of an equilateral triangle of side , d. Calculate the potential energy of the system

Three particles each of mass m are placed at the comers of an equilateral triangle of side , d. Calculate work done on this system if the side of the triangle is changed from d to 2d

Knowledge Check

  • (n-1) equal point masses each of mass m are placed at the vertices of a regular n-polygon. The vacant vertex has a position vector a with respect to the centre of the polygon. Find the position vector of centre of mass

    A
    `1/(n-1)a`
    B
    `-1/((n-1))a`
    C
    `(n-1)a`
    D
    `-((n-1)/a)`

  • Three identical spheres, each of mass m are placed at the corners of a right angled triangle with mutually perpendicular sides equal to 2m. Taking their point of intersection as the origin, the position vector of centre of mass is

    A
    `1/3(hat(i)-hat(j))`
    B
    `2/3(hat(i)-hat(j))`
    C
    `2/3(hat(i)+hat(j))`
    D
    `1/3(hat(i)+hat(j))`

  • Three identical spheres, each of mass m are placed at the corners of a right angled triangle with mutually perpendicular sides equal to 2m. Taking their point of intersection as the origin, the position vector of centre of mass is

    A
    `1/3(hati-hatj)`
    B
    `2/3(hati-hatj)`
    C
    `2/3(hati+hatj)`
    D
    `1/3(hati+hatj)`

    • Similar Questions

    Explore conceptually related problems

    Three equal particles each of mass m are placed at the three comers of as equilateral triangle of side A Find the force exerted by this system on another particle of mass m placed at (a) the mid-point of a side, (b) at the centre of the triangle.

    Three particles each of mass m are placed at the corners of an equilateral triangle of side d. Calculate (a) the potential energy of the system, (b) work done on this system if the side of the triangle is changed from dto 2d.

    Three particles of masses 100g, 150g and 200g are placed at the vertices of an equilateral triangle. Each side of the triangle is 0.5 m long. The centre of mass of the three particle is

    Three particles of masses 100 g, 150 g and 200.gare placed at the vertices of an equilateral triangle. Each side of the triangle is 0.5 m long. The centre of mass of the three particle is

    Four particles each of mass M, are located at the vertices of a square with side L. The gravitational potential due to this at the centre of the square is :

    Home
    Profile