This set of Mechatronics online test focuses on “Mechanical Actuating Systems – Degree of Freedom”.

1. What is Degree of freedom?

a) Total number of observations

b) Total number of independent constraints

c) Total number of observations minus the total number of independent constraints

d) Total number of independent constraints minus the total number of observations

View Answer

Explanation: Degree of Freedom is the total number of observations minus the total number of independent constraints. It defines the mobility and the possible number of movements that can be achieved by a system.

2. Degree of freedom is denoted by which Greek symbol?

a) α(alpha)

b) λ(lamda)

c) v(mu)

d) β(beta)

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Explanation: “Degrees of Freedom” is denoted by the Greek symbol ν (mu). The abbreviation “d.f” is commonly used to denote the degree of freedom in most of the books and writings. Degree of freedom is a quantity that represents the mobility of a system.

3. What is the statistical formula of degree of freedom? (where “df” represents degree of freedom and “n” represents the number of values in the sample set)

a) df = n^{2}

b) df = 2*n

c) df = n-1

d) df = (n^{2})-1

View Answer

Explanation: The statistical formula of degree of freedom is given by df=n-1 (where “df” represents degree of freedom and “n” represents the number of values in the sample set). In statistics degree of freedom represents that can be varied without violating the constraints.

4. What is the degree of freedom of a system, that has 5 variables and only 2 equations are known?

a) 3

b) 7

c) 1

d) 2

View Answer

Explanation: The degree of freedom can be found out by subtracting number of equations from number of variables. Degree of freedom is the number of independent variables that we can vary without violating the constraint. Here degree of freedom = 5(no. Of variable) – 2(no. of equation); therefore degree of freedom = 3.

5. Degree of freedom can be found out by subtracting number of equations from number of variables.

a) True

b) False

View Answer

Explanation: Degree of freedom can be found out by subtracting number of equations from number of variables. Degree of freedom is the number of independent variables that can be varied without violating the constraints. So by subtracting number of equations from number of variables we can get the number of independent variables.

6. The degree of freedom of all the gases is same.

a) True

b) False

View Answer

Explanation: The degree of freedom of all the gases is not same. It depends on the number of atoms present in a molecule. The degree of freedom for mono-atomic gases is 3, for di-atomic gases it is 5 and for tri-atomic gases it is 6.

7. How many degrees of freedom are present in a bionic arm?

a) 2

b) 3

c) 6

d) 7

View Answer

Explanation: Bionic arm consists of 7 degrees of freedom. The 7 degrees of freedom include shoulder joint that has 3 degrees of freedom, elbow joint has 1 degree of freedom, forearm with 1 degree of freedom and wrist with 2 degrees of freedom.

8. What will be the degree of freedom for two given independent samples whose sizes are N1 and N2 respectively?

a) N1+N2

b) N1-N2

c) (N1+N2)-2

d) (N1-N2)/2

View Answer

Explanation: The degree of freedom for two given independent samples whose sizes are N1 and N2 respectively is given by (N1+N2)-2. This method is mostly used while statistical calculating of the degree of freedom.

9. What is the degree of freedom of mono-atomic gases?

a) 1

b) 2

c) 3

d) 4

View Answer

Explanation: The degree of freedom of mono-atomic gases is 3. Mono-atomic gases have only one atom in the molecule. This molecule can move in any direction in the space; therefore it has 3 degrees of freedom.

10. What is the degree of freedom of a system, that has 5 variables and only 3 equations are known?

a) 3

b) 7

c) 2

d) 5

View Answer

Explanation: The degree of freedom can be found out by subtracting number of equations from number of variables. Degree of freedom is the number of independent variables that we can vary without violating the constraint. Here degree of freedom = 5(no. Of variable) – 3(no. of equation); therefore degree of freedom = 2.

11. What is the degree of freedom of a system, that has 5 variables and only 4 equations are known?

a) 3

b) 7

c) 1

d) 2

View Answer

Explanation: The degree of freedom can be found out by subtracting number of equations from number of variables. Degree of freedom is the number of independent variables that we can vary without violating the constraint. Here degree of freedom = 5(no. Of variable) – 4(no. of equation); therefore degree of freedom = 1.

12. What is the degree of freedom of di-atomic gases?

a) 6

b) 5

c) 3

d) 4

View Answer

Explanation: The degree of freedom of di-atomic gases is 5. Di-atomic gases have two atoms in the molecule. This molecule can move in any direction in the space; therefore it has 3 translational degrees of freedom. Also it can rotate in clockwise or anti clockwise direction which gives it additional 2 rotational degrees of freedom. So it has total 5 degrees of freedom.

13. What is the degree of freedom of tri-atomic gases?

a) 6

b) 5

c) 3

d) 4

View Answer

Explanation: The degree of freedom of tri -atomic gases is 6. Tri -atomic gases have three atoms in the molecule. This molecule can rotate in clockwise or anti clockwise direction from any of the three co-ordinate axis. So it has total 6 degrees of freedom.

14. What is the degree of freedom of Ozone?

a) 6

b) 5

c) 3

d) 4

View Answer

Explanation: The degree of freedom of Ozone gases is 6. The six degrees of freedom constitute of three rotational degrees of freedom and three translational degrees of freedom. Ozone is a tri-atomic molecule and the atoms are arranged in non-linear fashion.

15. What is the degree of freedom of Oxygen molecule?

a) 6

b) 5

c) 3

d) 4

View Answer

Explanation: The degree of freedom of Oxygen molecule is 5. The five degrees of freedom constitute of two rotational degrees of freedom and three translational degrees of freedom. The molecular formula of oxygen is O2, so it a diatomic molecule and hence the degree of freedom is 5.

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