Position vector of centre of two particles of masses `m_(1)` and `m_(2)` whose position vectors `r_(1)` and `r_(2)` then `r_(cm)`?

The centre of mass of a body is a point at which the entire mass of the body is supposed to be concentrated. The position vector overset rarr(r ) of c.m of the system of tow particles of masses m_(1) and m_(2) with position vectors overset rarr(r_(1)) and overset rarr(r_(2)) is given by overset rarr(r ) = (m_(1)overset rarr(r_(1)) + m_(2)overset rarr(r_(2)))/(m_(1) + m_(2)) For an isolated system, where no external force is acting, overset rarr(v_(cm)) = constant Under no circumstances, the velocity of centre of mass of an isolated system can undergo a change With the help of the comprehension given above, choose the most appropriate alternative for each of the following questions : Two bodies of masses 1 kg and 2kg are located at (1, 2) and (-1, 3) respectively. the co-ordinates of the cetre of mass are :

The centre of mass of a body is a point at which the entire mass of the body is supposed to be concentrated. The position vector overset rarr(r ) of c.m of the system of tow particles of masses m_(1) and m_(2) with position vectors overset rarr(r_(1)) and overset rarr(r_(2)) is given by overset rarr(r ) = (m_(1)overset rarr(r_(1)) + m_(2)overset rarr(r_(2)))/(m_(1) + m_(2)) For an isolated system, where no external force is acting, overset rarr(v_(cm)) = constant Under no circumstances, the velocity of centre of mass of an isolated system can undergo a change With the help of the comprehension given above, choose the most appropriate alternative for each of the following questions : An electron and a proton move towards eachother with velocities v_(1) and v_(2) respectively. the velocity of their centre of mass is

The centre of mass of a body is a point at which the entire mass of the body is supposed to be concentrated. The position vector overset rarr(r ) of c.m of the system of tow particles of masses m_(1) and m_(2) with position vectors overset rarr(r_(1)) and overset rarr(r_(2)) is given by overset rarr(r ) = (m_(1)overset rarr(r_(1)) + m_(2)overset rarr(r_(2)))/(m_(1) + m_(2)) For an isolated system, where no external force is acting, overset rarr(v_(cm)) = constant Under no circumstances, the velocity of centre of mass of an isolated system can undergo a change With the help of the comprehension given above, choose the most appropriate alternative for each of the following questions : A bomb dropped from an aeroplane in level flight explodes in the middle. the centre of mass of the fragments

The centre of mass of a body is a point at which the entire mass of the body is supposed to be concentrated. The position vector overset rarr(r ) of c.m of the system of tow particles of masses m_(1) and m_(2) with position vectors overset rarr(r_(1)) and overset rarr(r_(2)) is given by overset rarr(r ) = (m_(1)overset rarr(r_(1)) + m_(2)overset rarr(r_(2)))/(m_(1) + m_(2)) For an isolated system, where no external force is acting, overset rarr(v_(cm)) = constant Under no circumstances, the velocity of centre of mass of an isolated system can undergo a change With the help of the comprehension given above, choose the most appropriate alternative for each of the following questions : Two bocls of masses 5 kg and 2 kg are placed on a frictionless surface and connected by a spring. an external kick gives a velocity of 14 m//s to heavier block in the direction of lengter one. the velocity gained by the centre of mass is

What is the position vector of centre of mass of two particles of equal masses ?

If vec(R)_(CM) is the position of the centre of mass of a system of two particles of masses m_(1) and m_(2) then vec(R)_(CM) is given by :

Supposing Newton's law of gravitation for gravitation force F_(1) and F_(2) between two masses m_(1) and m_(2) at positions r_(1) and r_(2) read F_(2)=-F_(2)=(r_(12))/(r_(12)^(3))GM_(0)^(2)((m_(1)m_(2))/(M_(0)^(2)))^(n) where M_(0) is a constant dimension of mass, r_(12)=r_(1)-r_(2) and n is number. In such a case.

Supposing Newton's law of gravitation for gravitation forces F_(1) and F_(2) between two masses m_(1) and m_(2) at positions r_(1) and r_(2) read where M_(0) is a constant of dimension of mass, r_(12) = r_(1) - r_(2) and n is a number. In such a case,

The position vectors of three particles of mass m_(1) = 1kg, m_(2) = 2kg and m_(3) = 3kg are r_(1) = (hat(i) + 4hat(j) +hat(k)) m, r_(2) = (hat(i)+hat(j)+hat(k)) m and r_(3) = (2hat(i) - hat(j) -hat2k) m, respectively. Find the position vector of their center of mass.

The position of centre of mass of a system consisting of two particles of masses m_(1) and m_(2) seperated by a distance L apart , from m_(1) will be :