If all the particle of a system lie in X-Y plane is it necessary that the centre of mass be in X-Y plane?

The centre of mass is defined as vecR=1/Msum_im_ivecr_i . Suppose we define centre of charge as vecR_c=1/Qsum_iq_Ivecr_i where q_i represents the ith charge placed at vecr_i and Q is the total charge of the sytem a. Can a centre of charge of two charge system be outside the line segment joining the charges? b. If all the charges of a system are in X-Y plane? c. If all the charges of a system lie in a cube, is it necessary that the centre of charge be in the cube?

A small particle of mass on is projected with an initial velocity v at an angle 8 with x axis in X-Y plane as shown in Figure. Find the angular momentum of the particle.

The sphere shown in figure lies on a rough plane when a particle of mass m travelling at a speed v_0 collides and sticks with it. If the line of motion of the particle is at a distance h above the plane, find a. the linear speed o the combined system just after the collision b. the angular speed of the system about the centre of the sphere just the collision c. the value of h for which the sphere starts pure rolling on the plane Assume that the mass M of the sphere is large compared to the mass of the particle so that the centre of mass of the combined system is not appreciably shifted from the centre of the sphere.

A particle p moves from the point A(0,4) to the point 10 ,-4) . The particle P can travel the upper-half plane {(x , y)|yge0} at the speed of 1m//s and the lower-half plane {(x , y)|ylt=0} at the speed of 2 m/s. The coordinates of a point on the x-axis, if the sum of the squares of the travel times of the upper- and lower-half planes is minimum, are (a)(1, 0) (b) (2, 0) (c) (4, 0) (d) (5, 0)

The centre of mass of a system of particles is at the origin. It follows that:

Let the equations of a line and plane be (x+3)/2=(y-4)/3=(z+5)/2a n d4x-2y-z=1, respectively, then a. the line is parallel to the plane b. the line is perpendicular to the plane c. the line lies in the plane d. none of these

The x-y plane is rotated about its line of intersection with the y-z plane by 45^0 , then the equation of the new plane is/are a. z+x=0 b. z-y=0 c. x+y+z=0 d. z-x=0

Let the equation of the plane containing the line x-y - z -4=0=x+y+ 2z-4 and is parallel to the line of intersection of the planes 2x + 3y +z=1 and x + 3y + 2z = 2 be x + Ay + Bz + C=0 Compute the value of |A+B+C| .