Question

The weight of the hen is $1\dfrac{5}{6}$ then find the weight of the dog.

(A) $1 \dfrac{5}{4} k g$
(B) $1 \dfrac{7}{8} k g$
(C) $\dfrac{5}{4} k g$
(D) $\dfrac{8}{9} k g$

Answer 1

Hint: We know that the center of mass is a position defined relative to an object or system of objects. It is the average position of all the parts of the system, weighted according to their masses. For simple rigid objects with uniform density, the center of mass is located at the centroid. The centre of mass of an object is the point at which the object can be balanced. The centre of mass is useful because problems can often be simplified by treating a collection of masses as one mass at their common centre of mass. The weight of the object then acts through this point. The velocity of the system's center of mass does not change, as long as the system is closed. The system moves as if all the mass is concentrated at a single point. The final location will be at the weighted distance between the masses.

Complete step by step answer
To maintain the balanced condition, it is required to have equal weight on both the sides of the balance.
From the first instance we can see that the weight of the hen is given as $1\dfrac{5}{6}$kg or we can say $\dfrac{11}{6}kg$.
In order to maintain the balance, the weight of hen should be equal to the addition of the weights of the ball and fox. So, we can find the weight of the fox as:
$\dfrac{11}{6}-\dfrac{1}{12}=\dfrac{21}{12}=1\dfrac{9}{12}kg$
Now moving on to the second situation.
The weight of the dog will be equal to the addition of the weights of the ball and the fox. So, the weight of the dog is as follows:
$\dfrac{21}{12}+\dfrac{1}{8}=\dfrac{168+12}{96}=\dfrac{180}{96}=\dfrac{15}{8}=1\dfrac{7}{8}kg$

Hence the correct option is option B.

Note Thus, we can say that the centre of mass is the point at which the distribution of mass is equal in all directions, and does not depend on the gravitational field. Centre of gravity is the point at which the distribution of weight is equal in all directions, and does depend on the gravitational field. The centre of gravity (COG) of the human body is a hypothetical point around which the force of gravity appears to act. It is the point at which the combined mass of the body appears to be concentrated. Because it is a hypothetical point, the COG need not lie within the physical bounds of an object or person.