Legal Metrology • Paper-I
For free expansion of the gas which of the following is true (Q = heat supplied, W = workdone, Delta E_int = change in internal energy)
A)
Q = W = 0 and Delta E_int = 0
B)
Q = 0, W > 0 and Delta E_int = -W
C)
W = 0, Q > 0 and Delta E_int = -Q
D)
W > 0, Q < 0 and Delta E_int = 0
Based on established principles in Mechanical Engineering, the correct and most appropriate choice is 'W > 0, Q < 0 and Delta E_int = 0' (Option D).
Legal Metrology • Paper-I
A monoatomic gas of n-moles is heated from temperature T1 and T2 under two different conditions (i) at constant volume and (ii) at constant pressure. The change in internal energy of the gas is
A)
More for (i)
B)
More for (ii)
C)
Same in both cases
D)
Independent of number of moles
Based on established principles in Mechanical Engineering, the correct and most appropriate choice is 'More for (ii)' (Option B).
Legal Metrology • Paper-I
The equation of a SHM is y = 8sin(2x - 40t), where the distances and time are in cm and second respectively. The speed of the wave is
A)
2 cm/sec
B)
20 cm/sec
C)
30 cm/sec
D)
40 cm/sec
Based on established principles in the relevant subject area, the correct and most appropriate choice is '20 cm/sec' (Option B).
Legal Metrology • Paper-I
In a tug-of-war-contest. Two men pull on a horizontal rope from opposite sides. The winner will be the man who
A)
Exerts greater force on the rope
B)
Exerts greater force on the ground
C)
Exerts a force on the rope which is greater than the tension in the rope
D)
Makes a small angle with the vertical
Based on established principles in the relevant subject area, the correct and most appropriate choice is 'Exerts a force on the rope which is greater than the tension in the rope' (Option C).
Legal Metrology • Paper-I
A spring, which is initially in its unstretched condition, is first stretched by a length x and then again by a further length x. The work done in the first case is W1 and in the second case is W2.
A)
W1 = W2
B)
W2 = 2W1
C)
W2 = 3W1
D)
W2 = 4W1
Based on established principles in the relevant subject area, the correct and most appropriate choice is 'W2 = 2W1' (Option B).
Legal Metrology • Paper-I
If F represents force, A represents area and t represents time, then which of the following quantities has the same dimensions as the coefficient of viscosity eta?
A)
FA / t
B)
Ft / A
C)
FtA
D)
F / At
Based on established principles in the relevant subject area, the correct and most appropriate choice is 'F / At' (Option D).
Legal Metrology • Paper-I
One mole of an ideal monoatomic gas requires 210 J heat to raise the temperature by 10 K, when heated at constant pressure. If the same gas is heated at constant volume to raise the temperature by 10 K then heat required is
A)
126 J
B)
210 J
C)
146 J
D)
326 J
Based on established principles in Mechanical Engineering, the correct and most appropriate choice is '326 J' (Option D).
Legal Metrology • Paper-I
In a cyclic process, work done by the system is
A)
Zero
B)
Equal to heat given to the system
C)
More than the heat given to system
D)
Independent of heat given to the system
Based on established principles in Mechanical Engineering, the correct and most appropriate choice is 'Independent of heat given to the system' (Option D).
Legal Metrology • Paper-I
The third overtone of an open organ pipe of length l has the same frequency as the third overtone of a closed pipe of length l0. The ratio l / l0 is equal to
A)
2
B)
3/2
C)
5/3
D)
8/7
Correct option: D — 8/7. This matches the standard definition/result for the stated question.
Legal Metrology • Paper-I
Two identical samples of a gas are allowed to expand isothermally and adiabatically. Work done is
A)
More in the isothermal process
B)
More in the adiabatic process
C)
Neither of them
D)
Equal in both processes
Based on established principles in Mechanical Engineering, the correct and most appropriate choice is 'More in the adiabatic process' (Option B).
Legal Metrology • Paper-I
The ratio of specific heats Cp/Cv of CO is
A)
1.33
B)
1.40
C)
1.65
D)
1.21
Based on established principles in Mechanical Engineering, the correct and most appropriate choice is '1.65' (Option C).
Legal Metrology • Paper-I
When the potential energy of a particle executing simple harmonic motion is one-fourth of its maximum value during the oscillation, the displacement of the particle from the equilibrium position in terms of its amplitude alpha is
A)
alpha/4
B)
alpha/3
C)
alpha/2
D)
alpha
Based on established principles in the relevant subject area, the correct and most appropriate choice is 'alpha/3' (Option B).
Legal Metrology • Paper-I
A particle moves in a straight line with a retardation proportional to its displacement. Its loss of kinetic energy for an displacement x is proportional to
A)
x
B)
x^2
C)
ln x
D)
e^x
Based on established principles in the relevant subject area, the correct and most appropriate choice is 'x' (Option A).
Legal Metrology • Paper-I
In a refrigerator, the low temperature coils are at a temperature of – 23o C and the compressed gas in the condenser has a temperature of 27o C. The theoretical coefficient of performance is
A)
5
B)
6
C)
7
D)
8
Based on established principles in Mechanical Engineering, the correct and most appropriate choice is '7' (Option C).
Legal Metrology • Paper-I
The total energy of a particle executing SHM is
A)
Directly proportional to x
B)
Directly proportional to x^2
C)
Independent of x
D)
Directly proportional to x^1/2
Based on established principles in the relevant subject area, the correct and most appropriate choice is 'Directly proportional to x^1/2' (Option D).
Legal Metrology • Paper-I
In a given process for an ideal gas, dW = 0 and dQ < 0. Then for the gas
A)
The temperature will decrease
B)
The volume will increase
C)
The pressure will remain constant
D)
The temperature will increase
Based on established principles in Mechanical Engineering, the correct and most appropriate choice is 'The temperature will decrease' (Option A).
Legal Metrology • Paper-I
The acceleration of a particle performing SHM is 12cm/sec^2 at a distance of 3cm from the mean position. Its time period is
A)
0.5 sec
B)
1.0 sec
C)
2.2 sec
D)
3.14 sec
Based on established principles in the relevant subject area, the correct and most appropriate choice is '3.14 sec' (Option D).
Legal Metrology • Paper-I
For a reversible process, necessary condition is
A)
In the whole cycle of the system, the loss of any type of heat energy should be zero
B)
That the process should be too fast
C)
That the process should be slow so that the working substance should remain in thermal and mechanical equilibrium with the surroundings
D)
The loss of energy should be zero and it should be quasistatic
Based on established principles in Mechanical Engineering, the correct and most appropriate choice is 'In the whole cycle of the system, the loss of any type of heat energy should be zero' (Option A).
Legal Metrology • Paper-I
A spherical black body with a radius of 12 cm radiates 450 W power at 500K. If the radius were halved and the temperature doubled, the power radiated in watts would be
A)
225
B)
450
C)
900
D)
1800
For the stated ideal FM relation, doubling bandwidth/deviation improves the SNR by about fourfold.
Legal Metrology • Paper-I
When cooking oil is heated in a frying pan, the oil moves around in the pan more easily when it is hot. The main reason for this is that with rise in temperature, there is a decrease in
A)
surface tension
B)
viscocity
C)
angle of contact
D)
density
Based on established principles in the relevant subject area, the correct and most appropriate choice is 'viscocity' (Option B).
Legal Metrology • Paper-I
Two springs of constant k1 and k2 are joined in series. The effective spring constant of the combination is given by
A)
k1(k2 + k1)
B)
(k1 k2) / (k1 + k2)
C)
k1 + k2
D)
1 / (k1 + k2)
Based on established principles in the relevant subject area, the correct and most appropriate choice is 'k1(k2 + k1)' (Option A).
Legal Metrology • Paper-I
The potential energy of a molecule on the surface of liquid compared to one inside the liquid is
A)
Zero
B)
Smaller
C)
Greater
D)
The same
Based on established principles in the relevant subject area, the correct and most appropriate choice is 'Zero' (Option A).
Legal Metrology • Paper-I
Small liquid drops assume spherical shape because
A)
Atmospheric pressure exerts a force on a liquid drop
B)
Volume of a spherical drop is minimum
C)
Gravitational force acts upon the drop
D)
Liquid tends to have the minimum surface area due to surface tension
Based on established principles in the relevant subject area, the correct and most appropriate choice is 'Volume of a spherical drop is minimum' (Option B).
Legal Metrology • Paper-I
A liquid drop at temperature t, isolated from its surroundings, breaks into a number of droplets. The temperature of the droplets will be
A)
equal to t
B)
greater than t
C)
less than t
D)
either (a), (b) or (c) depending on the surface tension of the liquid
Based on established principles in the relevant subject area, the correct and most appropriate choice is 'greater than t' (Option B).
Legal Metrology • Paper-I
The Bulk modulus for an incompressible liquid is
A)
Zero
B)
Unity
C)
Infinity
D)
Between 0 to 1
Based on established principles in the relevant subject area, the correct and most appropriate choice is 'Zero' (Option A).
