Question

masses 1kg 1.5kg 2kg and M kg are situated at (2,1,1),(1,2,1),(2,-2,1),(-1,4,3). if their centre of mass is situated at (1,1,3/2), the value of M is​

Answer 1

Answer:

The value of M is 1.5 Kg

Explanation:

Given data:

M1 = 1 Kg ,  (2,1,1)

M2 = 1.5kg , (1,2,1)

M3 =  2kg  , (2,-2,1)

M4 =  M kg , (-1,4,3)

(x , y , z ) = (1,1,3/2)  <= Location of centre of mass

Now

x  = m1x1 + m2x2 + m3x3 + m4x4/ m1 + m2 + m3 + m4

  1 = 1 x 2 + 1.5 x 1 + 2 x 2 + M x (-1) / 1 + 1.5 + 2 + M

  1 = 7.5 - M/ 4.5 + M

=> 4.5 + M = 7.5 - M

    2 M = 3

    M = 3/2 = 1.5 Kg

Answer 2

Answer:

the value of M is 1.5 kg

Explanation:

Correct answer is (b) 1.5 kg

The explanation is: Sum of masses = 1 + 1.5 + 2 + M = 4.5 + M

x-coordinate;

(1*2 + 1.5*1 + 2*2 – M)/(4.5 + M) = 1

4.5 + M = 7.5 – M

2M = 3

M = 1.5 kg.