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Units and Measurements

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

Answer

(4) The dimensions of n/ is [T]

Solution

the argument of sin and cos is dimensionless:

(A): nt dimensionless [nt]=[ ]=[L] (A) is correct

(B): [n]= [L][T]=[ LT-1] (B) is correct

(C): x dimensionless [x]=[L] (C) is correct

(D): [ n ]= [ LT-1][L]=[ T-1], not [T] (D) is NOT correct

Answer: (4)

Keep practising — Units and Measurements

Ques. 2JEE 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. 3JEE 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. 4JEE 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. 5JEE 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. 6JEE 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. 7JEE 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. 8JEE 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. 9JEE 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. 10JEE 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. 11JEE 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)

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