Question

(i) Where is the centre of gravity of a uniform ring situated?
(ii) “The position of the centre of gravity of a body remains unchanged even when the body is deformed”. State whether this statement is true or false.

Answer 1

Hint: The center of gravity of an object is defined as the point at which the weight is evenly dispersed and all sides are in balance. To solve the given question, we will apply the concept of center of gravity to find the required correct answer.

Complete step by step answer:
(i) Centre of gravity of an object is calculated by taking the sum of the moments divided by the overall weight of the object. The moment of the object is given by the product of its weight and the location of the object which is taken as the origin.
Centre of gravity of a uniform body is the same as the centre of mass. The centre of gravity for regular bodies lies at the centre of the body. Therefore, the centre of gravity of a uniform ring is situated at the centre of the ring.
(ii) Stability of the object is affected by the position of the centre of the gravity. Lower the centre of gravity of the object, more stable the object is. So, the position of the centre of the gravity changes when a body is deformed. Therefore, the given statement “The position of the centre of gravity of a body remains unchanged even when the body is deformed” is false.
Hence, (i) The centre of gravity of a uniform ring is situated at the centre of the ring. (ii) The given statement is false.

Note:
The centre of gravity is defined as the point at which the net gravitational force on an object is assumed to be acting on it. Generally, the gravitational force does not vary much over the dimensions of a normal object on the earth. Since, the gravitational field is uniform near and around the earth. In practice, centre of gravity and centre of mass are coincident for normal objects with uniform density on the earth.