Question

particle 13.9 A particle of mass 3m is located 1.00 m from a of mass m. (a) Where should you put a third mass M so that the ull of the sun on net gravitational force on M due to the two masses is exactly zero? ume the distance (b) Is the equilibrium of M at this point stable or unstable () for y the distance of points along the line connecting m and 3m, and (ii) for points dix F. Is it more along the line passing through M and perpendicular to the line or that the moon connecting m and 3m?

Answer 1

Part (a): since we know that Gravitational force is central line force & which is always attractive in nature. Let us take force F_1 is gravitational force on M due to mass m & F_2 is gravitational force on M due to mass 3m. Let us assume at point p net gravitational force on M is zero. Therefore F_1 = F_2 G middot m times M/x^2 = G middot 3m middot M/(1 - x)^2 1/x^2 = 3/(1 - x^2) {therefore Gravitational force b/w two masses F = G m_1 m_2/r^2} 1 - x^2 = 3x^2 1 = 4x^2 x = 1/2 \r\n part (b): (i) equilibrium along the line connecting m & 3m If we disturb M towards mass m, it will be attracted by m since F_1 will b greater than F_2, If we there is unstable equilibrium (ii) equilibrium along the line passing through M & perpendicular to the line connecting m & 3m from the diagram, if is evident there