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Units and Measurements

JEE Main 2024 (Online) 6th April Evening ShiftMCQEasy📈 Topic in 53% papers+4−1
Ques. 1JEE Main 2024, 6 April (Evening Shift)

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

Answer

(4) Statement (I) is correct but statement (II) is incorrect

Solution

Statement I: Q = mc T [c] = [Q][m][ T] = ML2T-2M K

[c] = [ L2 T-2 K-1] ⇒ Statement I is correct

Statement II: PV = nRT [R] = [PV][n][T] = ML2T-2mol K

[R] = [ M L2 T-2 K-1 mol-1]

the power of T is -2 (not -1) ⇒ Statement II is incorrect

Answer: (4)

Keep practising — Units and Measurements

Ques. 2JEE Main 2024, 6 April (Evening Shift)

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
Ques. 3JEE Main 2024, 5 April (Morning Shift)

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
Ques. 4JEE Main 2024, 5 April (Morning Shift)

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
Ques. 5JEE Main 2024, 5 April (Evening Shift)

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]
Ques. 6JEE Main 2024, 5 April (Evening Shift)

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
Ques. 7JEE Main 2024, 4 April (Morning Shift)

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]
Ques. 8JEE Main 2024, 4 April (Evening Shift)

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
Ques. 9JEE Main 2024, 1 February (Morning Shift)

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
Ques. 10JEE Main 2024, 1 February (Morning Shift)

The dimensional formula of angular impulse is :

  1. [ ML2T-2]
  2. [ ML-2T-1]
  3. [ ML2T-1]
  4. [ MLT-1]
Ques. 11JEE Main 2024, 1 February (Morning Shift)

The radius (r), length (l) and resistance (R) of a metal wire was measured in the laboratory as r=(0.35 0.05) cm R=(100 10) ohm l=(15 0.2) cm The percentage error in resistivity of the material of the wire is :

  1. 37.3\%
  2. 25.6\%
  3. 35.6\%
  4. 39.9\%

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