The density of a material in the shape of a cube is determined by measuring three sides of the cube and its mass. If the relative errors in measuring the mass and length are respectively 1.5% and 1%, the maximum error in determining the density is:

  1. 3.5%
  2. 4.5%
  3. 6%
  4. 2.5%

Which one of the following represents the correct dimensions of the coefficient of viscosity?

  1. ML-2T-2
  2. MLT-1
  3. ML-1T-1
  4. ML-1T-2

Dimensions of 1/μoεo, where symbols have their usual meaning, are

  1. [L2T–2]
  2. [LT–1]
  3. [L–2T2]
  4. [L–1T]

Which of the following units denotes the dimensions ML2/Q2, where Q denotes the electric charge?

  1. weber (Wb)
  2. H/m2
  3. Wb/m2
  4. henry (H)

The physical quantities not having same dimensions are

  1. torque and work
  2. stress and Young's modulus
  3. speed and (μ0ε0)–1/2
  4. momentum and Planck's constant

Identify the pair whose dimensions are equal

  1. force and work
  2. torque and work
  3. stress and energy
  4. force and stress

The dimension of magnetic field in M, L, T and C (coulomb) is given as

  1. MT–1C–1
  2. MLT–1C–1
  3. MT2C–2
  4. MT–2C–1

The velocity of a particle depends upon t as V = A + Bt + ct2. If velocity is in m/s, the unit of A will be

  1. m/s
  2. m/s2
  3. m.s
  4. m2/s

Which of the following pairs does not have the same dimensions?

  1. frequency and angular frequency
  2. angular velocity and velocity gradient
  3. velocity gradient and angular frequency
  4. angular frequency and potential energy gradient