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 : 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

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

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) ?

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 :

Fill in the blanks : (i) overset rarr(tau) = overset rarr(r ) xx … (ii) overset rarr(L) = overset rarr(r ) xx …

If overset rarr A + overset rarr B = overset rarr A - overset rarr B ,then:

Show that |overset rarr A + overset rarr B|^2 - |overset rarr A - overset rarr B |^2 = 4 overset rarr A cdot overset rarr B .

Show that the area of the triangle contained between the vector overset rarr(r ) and overset rarr(b) is one half of the magnitude of overset rarr(a) xx overset rarr(b)

Show that the area of the triangle contained between the vector overset rarr(a ) and overset rarr(b) is one half of the magnitude of overset rarr(a) xx overset rarr(b)