Units and Measurements

While measuring diameter of wire using screw gauge the following readings were noted. Main scale reading is 1 mm and circular scale reading is equal to 42 divisions. Pitch of screw gauge is 1 mm and it has 100 divisions on circular scale. The diameter of the wire is x50 mm. The value of x is :

1. 42
2. 71
3. 21
4. 142

Given below are two statements: In the light of the above statements, choose the most appropriate answer from the options given below.

1. Statement (I) is incorrect but statement (II) is correct
2. Both statement (I) and statement (II) are incorrect
3. Both statement (I) and statement (II) are correct
4. Statement (I) is correct but statement (II) is incorrect

In a vernier calliper, when both jaws touch each other, zero of the vernier scale shifts towards left and its 4th division coincides exactly with a certain division on main scale. If 50 vernier scale divisions equal to 49 main scale divisions and zero error in the instrument is 0.04 mm then how many main scale divisions are there in 1 cm ?

1. 5
2. 40
3. 10
4. 20

If G be the gravitational constant and u be the energy density then which of the following quantity have the dimensions as that of the uG :

1. Gravitational potential
2. pressure gradient per unit mass
3. Energy per unit mass
4. Force per unit mass

Time periods of oscillation of the same simple pendulum measured using four different measuring clocks were recorded as 4.62 s, 4.632 s, 4.6 s and 4.64 s. The arithmetic mean of these readings in correct significant figure is :

1. 5 s
2. 4.6 s
3. 4.62 s
4. 4.623 s

What is the dimensional formula of ab-1 in the equation (P + aV2 )(V - b) = RT, where letters have their usual meaning.

1. [M6 L7 T4]
2. [ M-1 L5 T3]
3. [ M0 L3 T-2]
4. [ M L2 T-2]

A vernier callipers has 20 divisions on the vernier scale, which coincides with 19th division on the main scale. The least count of the instrument is 0.1 mm. One main scale division is equal to mm.

1. 5
2. 2
3. 1
4. 0.5

The equation of stationary wave is : y=2a ( 2 ) ( 2 x ). Which of the following is NOT correct :

1. The dimensions of nt is [L]
2. The dimensions of n is [ LT-1]
3. The dimensions of x is [L]
4. The dimensions of n/ is [T]

Applying the principle of homogeneity of dimensions, determine which one is correct, where T is time period, G is gravitational constant, M is mass, r is radius of orbit.

1. T2 = 4 2 rGM2
2. T2 = 4 2 r3
3. T2 = 4 2 r3GM
4. T2 = 4 2 r2GM

10 divisions on the main scale of a Vernier calliper coincide with 11 divisions on the Vernier scale. If each division on the main scale is of 5 units, the least count of the instrument is :

1. 511
2. 1011
3. 5011
4. 12