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NTA Abhyas 2020
Exam
NTA Abhyas
Year
2020
Subject
Physics
Chapter
Units and Dimensions

NTA Abhyas 2020 · Physics · Units and Dimensions

In the formula, a = 3bc^ 2 , a and c have dimensions of electric...

In the formula, a=3bc2a = 3bc^{2}, aa and cc have dimensions of electric capacitance and magnetic field intensity respectively. The dimensions of bb in S.I.S. I. system are

Options

  1. A[M−3L−2T4Q4][ M^{- 3}L^{- 2}T^{4}Q^{4} ]
  2. B[M−3T4Q4][ M^{- 3}T^{4}Q^{4} ]
  3. C[M−3T3Q][ M^{- 3}T^{3}Q ]
  4. D[M−3L2T4Q−4][ M^{- 3}L^{2}T^{4}Q^{- 4} ]

Correct answer

A. [M−3L−2T4Q4][ M^{- 3}L^{- 2}T^{4}Q^{4} ]

Step-by-step solution

Given, a=3bc2a = 3bc^{2}

⇒b=a3c2⇒ b = \dfrac{a}{3c^{2}}

Writing dimensions for aandca and c, we have

\left[b\right] = \left[Q / V\right]\left[B\right]2 = \dfrac{\left[Q\right] [ ML^{2}T^{- 2}Q^{- 1}{]}^{- 1}}{\left[MT^{- 1}Q^{- 1}\right]2}<br/><br/><br /><br />= [ M^{- 3}L^{- 2}T^{4}Q^{4} ]
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