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There are two masses m1 , and m2 are placed at a distance l apart, let the centre of mass of this system is at a point named m1 is displaced by l1towards C and m2 is displaced by I2away from C. Find the distance, from C where new centre ofmass will be located.?
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There are two masses m1 , and m2 are placed at a distance l apart, let...
Problem Analysis:
We are given two masses m1 and m2 placed at a distance l apart. The center of mass of this system is initially at a point C. Now, m1 is displaced by l1 towards C and m2 is displaced by l2 away from C. We need to find the new distance of the center of mass from point C.

Solution:
Let's consider the initial position of the center of mass as x1 from point C. Since the total mass of the system is the sum of m1 and m2, the center of mass can be calculated using the formula:

x1 = (m1 * 0 + m2 * l) / (m1 + m2)


Now, after the displacement, the new position of m1 will be l1 towards C, so the new position of m1 will be (x1 - l1). Similarly, the new position of m2 will be l2 away from C, so the new position of m2 will be (x1 + l2).

The new center of mass can be calculated using the formula:

x2 = (m1 * (x1 - l1) + m2 * (x1 + l2)) / (m1 + m2)


Simplifying the above equation, we get:

x2 = (m1 * x1 - m1 * l1 + m2 * x1 + m2 * l2) / (m1 + m2)


Now, let's substitute the value of x1 from the initial equation:

x2 = (m1 * ( (m1 * 0 + m2 * l) / (m1 + m2) ) - m1 * l1 + m2 * ( (m1 * 0 + m2 * l) / (m1 + m2) ) + m2 * l2) / (m1 + m2)


Simplifying further, we get:

x2 = (m1 * m2 * l - m1 * l1 + m2 * m1 * l + m2 * l2) / (m1 + m2)^2


Hence, the new distance of the center of mass from point C is given by:

x2 - x1 = (m1 * m2 * l - m1 * l1 + m2 * m1 * l + m2 * l2) / (m1 + m2)^2 - (m1 * 0 + m2 * l) / (m1 + m2)


Simplifying the above equation, we get:

x2 - x1 = (m1 * m2 * l - m1 * l1 + m2 * m1 * l + m2 * l2 - m2 * l) / (m1 + m2)^2


Hence, the new distance of the center of mass from point C is given by:

x2 - x1 = (m1 * m2 * l - m1 * l1 + m2 * m1 * l + m2 * l2 - m2 * l) / (m1 + m2)^2
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Position of centre of massIn a uniform gravitational field the centre of mass coincide with the centre of gravity. But these two points do not always coincide, however. For example, the Moon’s centre of mass is very close to its geometric centre (it is not exact because the Moon is not a perfect uniform spher e), but its centre of gravity is slightly displaced towards Earth because of the stronger gravitational force on the Moon’s near side facing the earth. If an object does not have a uniform weight distribution then the center of mass will be closer to where most of the weight is located. For example, the center of gravity for a hammer is located close to where the head connects to the handle. The center of mass can be located at an empty point in space, such as the center of a hollow ball. The center of gravity can even be completely outside of an object, such as for a donut or a curved banana.Standing upright, an adult human’s centre of mass is located roughly at the center of their torso. The centre of mass rises a few inches when with rising arms.The center of gravity can even be at a point outside the body, such as when bent over in an inverted-U pose.An object is in balanced position if its center of gravity is above its base of support. For the two cylinders below, the left cylinder’s CG is above the base of support so the upward support force from the base is aligned with the downward force of gravity. For the cylinder on the right the CG is not above the base of support so these two forces cannot align and instead create a torque that rotates the object, tipping it over.Does the centre of mass does not coincide with the centre of gravity of a body?

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There are two masses m1 , and m2 are placed at a distance l apart, let the centre of mass of this system is at a point named m1 is displaced by l1towards C and m2 is displaced by I2away from C. Find the distance, from C where new centre ofmass will be located.?
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There are two masses m1 , and m2 are placed at a distance l apart, let the centre of mass of this system is at a point named m1 is displaced by l1towards C and m2 is displaced by I2away from C. Find the distance, from C where new centre ofmass will be located.? for Class 11 2024 is part of Class 11 preparation. The Question and answers have been prepared according to the Class 11 exam syllabus. Information about There are two masses m1 , and m2 are placed at a distance l apart, let the centre of mass of this system is at a point named m1 is displaced by l1towards C and m2 is displaced by I2away from C. Find the distance, from C where new centre ofmass will be located.? covers all topics & solutions for Class 11 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for There are two masses m1 , and m2 are placed at a distance l apart, let the centre of mass of this system is at a point named m1 is displaced by l1towards C and m2 is displaced by I2away from C. Find the distance, from C where new centre ofmass will be located.?.
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