Home
Class 11
PHYSICS
Three portion A , B and C each of mass r...

Three portion A , B and C each of mass re placed ina line with AB=BC=d. Find the gravittional force on a fourth article P of same mass placed at a distance d from the particle B on the perpendicular bisector of the line AC.

Text Solution

Verified by Experts


The force ast P due to A is
`F_A=(Gm^2)/((AP)^2)=(Gm^2)/(2d^2)`
along PA. the force at P due to C is
`F_C=(Gm^2)/((CP)^2)=(Gm^2)/(2d^2)`
along PC. The force at P due to B is
`F_B=(Gm^2)/d^2` along PB
The resultant of `F_A,F_B and F_c` will be along PB. Clearly `/_APB=/_BPC=45^@`
Component of `F_A` and `PB=F_Acos5^@ =(Gm^2)/(2sqrt2d^2)`
component of `F_C` along `PB=F_Ccos45^@=(Gm^2)/(2sqrt2d^2)`
component of `F_B along PB=(Gm^2)/d^2`
Hence the resultant of three forces is
`(Gm^2)/d^2)1/(2sqrt2)+1/2sqrt2)+1)=(Gm^2)/d^2(1+1/sqrt2)` along PB.
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

Similar Questions

Explore conceptually related problems

A tunnel is dug along a diameter of the earth. Find the force on a particle of mass m placed in the tunnel at a distance x from the centre.

A particle of mass M is placed at the centre of a uniform spherical shell of equal mass and radius a. Find the gravitational potential at a point P at a distance a/2 from the centre.

Knowledge Check

  • Two particles each of mass 'm' are placed at A and C are such AB=BC=L . The gravitational force on the third particle placed at D at a distance L on the perpendicular bisector of the line AC is

    A
    `(Gm^(2))/(L^(2))` along `BD`
    B
    `(Gm^(2))/(sqrt(2)L^(2))` along `DB`
    C
    `(Gm^(2))/(L^(2))` along `AC`
    D
    `(Gm^(2))/(sqrt(2)L^(2))` along `BD`

  • Three equal masses each of mass 'm' are palced at the three corners of an equilateral of side a If a fourth particle of equal mass is placed at the centre of triangle then net force acting on it is equal to .

    A
    `(Gm^(2))/(a^(2))`
    B
    `(4Gm^(2))/(3a^(2))`
    C
    `(3Gm^(2))/(a^(2))`
    D
    zero

  • Three equal masses each of mass 'm' are placed at the three-corner of an equilateral triangle of side 'a' If a fourth particle of equal mass is placed at the centre of triangle, then rate force acting on it, is equal to

    A
    `(Gm^(2))/(a^(2))`
    B
    `(4Gm^(2))/(3a^(2))`
    C
    `(3Gm^(2))/(a^(2))`
    D
    zero

    • Similar Questions

    Explore conceptually related problems

    Three identical particles each of mass m are placed at the vertices of an equilateral triangle of side a. Fing the force exerted by this system on a particle P of mass m placed at the (a) the mid point of a side (b) centre of the triangle

    Three equal masses m are placed at the three corners of an equilateral tringle of side a. find the force exerted by this sytem on another particle of mass m placed at a. the mid point of a side b. at the centre of the triangle.

    A thin shell of mass m and radius R is fixed. Two particles of same mass m are fixed at point A and B on the shell such that AB subtends an angle of 120^(@) at the centre. A particle of mass m is held at point C inside the shell which is on perpendicular bisector of line AB. Find the velocity of mass at C when it reaches the opposite end of the point C on the shell under the influence of gravitational field.

    Two particles A and B having equal charges are placed at distance d apart. A third charged particle placed on the perpendicular bisector at a distance x will experience the maximum Coulomb’s force when :

    Two point masses, each equal to M, are placed a distance 2a apart. Show that a small mass m placed midway between them on the line joining them will be in equilibrium and if it is slightly displaced from this position along the line perpendicular to the line joining the masses, it will execute simple harmonic oscillations. Calculate the frequnency of these oscillations.

    Home
    Profile