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Units and Measurements

JEE Main 2024 (Online) 4th April Evening ShiftMCQEasy📈 Topic in 22% papers+4−1
Ques. 1JEE 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

Answer

(3) T2 = 4 2 r3GM

Solution

[G] = M-1L3T-2 and [T2] = T2 (4 2 is dimensionless)

(A): [ rGM2 ] = L M-1L3T-2 M2 = M-1L-2T2 ⇒ (A) is wrong

(B): [r3] = L3 ⇒ (B) is wrong

(C): [ r3GM ] = L3 M-1L3T-2 M = T2 ⇒ (C) is correct

(D): [ r2GM ] = L-1T2 ⇒ (D) is wrong

only in (C) both sides have the same dimensions (T2)

Answer: (3)

Keep practising — Units and Measurements

Ques. 2JEE 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. 3JEE 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. 4JEE 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\%
Ques. 5JEE Main 2024, 1 February (Evening Shift)

Match List - I with List - II. Choose the correct answer from the options given below :

  1. (A)-(II), (B)-(I), (C)-(IV), (D)-(III)
  2. (A)-(IV), (B)-(III), (C)-(I), (D)-(II)
  3. (A)-(I), (B)-(II), (C)-(III), (D)-(IV)
  4. (A)-(III), (B)-(IV), (C)-(II), (D)-(I)
Ques. 6JEE Main 2024, 31 January (Morning Shift)

If the percentage errors in measuring the length and the diameter of a wire are 0.1\% each. The percentage error in measuring its resistance will be:

  1. 0.144%
  2. 0.2%
  3. 0.1%
  4. 0.3%
Ques. 7JEE Main 2024, 31 January (Morning Shift)

A force is represented by F=ax2+bt 12 where x= distance and t= time. The dimensions of b2/a are:

  1. [ ML2 T-3 ]
  2. [ ML3 T-3 ]
  3. [ MLT-2 ]
  4. [ ML-1T-1 ]
Ques. 8JEE Main 2024, 31 January (Evening Shift)

Consider two physical quantities A and B related to each other as E= B-x2At where E, x and t have dimensions of energy, length and time respectively. The dimension of AB is

  1. L-2M1T0
  2. L2M-1T1
  3. L0M-1T1
  4. L-2M-1T1
Ques. 9JEE Main 2024, 31 January (Evening Shift)

The measured value of the length of a simple pendulum is 20 cm with 2 mm accuracy. The time for 50 oscillations was measured to be 40 seconds with 1 second resolution. From these measurements, the accuracy in the measurement of acceleration due to gravity is N%. The value of N is:

  1. 6
  2. 5
  3. 4
  4. 8
Ques. 10JEE Main 2024, 30 January (Morning Shift)

Match List I with List II. Choose the correct answer from the options given below :

  1. (A)-(II), (B)-(I), (C)-(IV), (D)-(III)
  2. (A)-(I), (B)-(II), (C)-(III), (D)-(IV)
  3. (A)-(IV), (B)-(III), (C)-(II), (D)-(I)
  4. (A)-(III), (B)-(IV), (C)-(II), (D)-(I)
Ques. 11JEE Main 2024, 30 January (Evening Shift)

If 50 Vernier divisions are equal to 49 main scale divisions of a traveling microscope and one smallest reading of main scale is 0.5 mm, the Vernier constant of traveling microscope is

  1. 0.01 mm
  2. 0.01 cm
  3. 0.1 mm
  4. 0.1 cm

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