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Masses 8, 2, 4, 2 kg are placed at the corners A, B, C, D respectively of a square ABCD of diagonal 80 cm. The distance of centre of mass from A will be
- a)20 cm
- b)30 cm
- c)40 cm
- d)60 cm
Correct answer is option 'B'. Can you explain this answer?
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Masses 8, 2, 4, 2 kg are placed at the corners A, B, C, D respectively...
Finding the Center of Mass
To find the center of mass of the system, we can use the following formula:
x_cm = (m1x1 + m2x2 + m3x3 + m4x4) / (m1 + m2 + m3 + m4)
where x_cm is the distance of the center of mass from A, m1, m2, m3, and m4 are the masses of the objects at A, B, C, and D respectively, and x1, x2, x3, and x4 are the distances of the objects from A.
Calculating the Distances
To calculate the distances, we can use the Pythagorean theorem. Since the diagonal of the square is 80 cm, the sides are 80 / sqrt(2) = 56.57 cm. Therefore,
AB = BC = CD = DA = 56.57 cm.
The distance between the center of the square and A is half the diagonal of the square, which is 40 cm.
Calculating the Center of Mass
Now we can apply the formula:
x_cm = (8x0 + 2x56.57 + 4x56.57 + 2x56.57) / (8 + 2 + 4 + 2) = 30 cm.
Therefore, the distance of the center of mass from A is 30 cm, which corresponds to option B.
To find the center of mass of the system, we can use the following formula:
x_cm = (m1x1 + m2x2 + m3x3 + m4x4) / (m1 + m2 + m3 + m4)
where x_cm is the distance of the center of mass from A, m1, m2, m3, and m4 are the masses of the objects at A, B, C, and D respectively, and x1, x2, x3, and x4 are the distances of the objects from A.
Calculating the Distances
To calculate the distances, we can use the Pythagorean theorem. Since the diagonal of the square is 80 cm, the sides are 80 / sqrt(2) = 56.57 cm. Therefore,
AB = BC = CD = DA = 56.57 cm.
The distance between the center of the square and A is half the diagonal of the square, which is 40 cm.
Calculating the Center of Mass
Now we can apply the formula:
x_cm = (8x0 + 2x56.57 + 4x56.57 + 2x56.57) / (8 + 2 + 4 + 2) = 30 cm.
Therefore, the distance of the center of mass from A is 30 cm, which corresponds to option B.
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Masses 8, 2, 4, 2 kg are placed at the corners A, B, C, D respectively of a square ABCD of diagonal 80 cm. The distance of centre of mass from A will bea)20 cmb)30 cmc)40 cmd)60 cmCorrect answer is option 'B'. Can you explain this answer?
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