Numerical based on Centre of Mass

Q1. Two particles of masses 2kg and 3kg are located at ( 2,3) and ( 1, -3) respectively. Calculate the co-ordinated of C.M.
Q2. Two-point objects of masses 1.5g and 2.5g are 16cm apart, the centre of mass is at a distance (x) from the object of mass 1.5g . Find the value of x.
Q3. The position vectors of three particles of masses m_1= 0.5kg, m_2 = 1kg and m_3= 1.5kg are r ⃗_1= ( i ̂ + 4j ̂+ k ̂)m, r ⃗_2 = i ̂ + 2j ̂+ 2k ̂)m and r ⃗_3 = ( i ̂ - 2j ̂-3k ̂)m, respectively. Find the position vector of their centre of mass.
Q4. Four particles of masses 1kg, 2kg, 3kg and 4kg are placed at four corners of vertices A, B, C and D of a square of side 1m as shown in figure. Find the co-ordinates of C.M. of mass.
Ans ( 0.5,0.3)
Q5. Three-point masses m_1= 2kg, m_2 = 3kg and m_3= 5kg are kept at the three corners of an equilateral triangle ABC respectively, of side 1m as shown in figure. Find centre of mass of three particle system. ( Ans ( 0.55, √3/4)
Q6. Find the position of centre of mass of uniform lamina as shown in figure, if a small disc of radius a/2 is cut from the disc of radius a
Q7. A small disc of radius 2cm is cut from a disc of radius 6cm. If the distance between their centres is 3.2cm, what is the shift in the centre of mass of the disc.
Q8. A straight rod of length L has one of its end at the origin and another end at x = L. If the mass per unit length of the rod is given by Ax, where A is constant. Where is the Centre of mass of the rod? Ans: ( 2/3 L,0,0)
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