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Physics · Units, Dimensions & Error Analysis

JEE Advanced 2019 — Paper 1 — Question 8

Let us consider a system of units in which mass and angular momentum are dimensionless. If length has dimension of L , which of the following statement(s) is/are correct?

  1. Option A:

    The dimension of energy is L−2\mathrm{L}^{-2}

    Correct
  2. Option B:

    The dimension of force is L−3\mathrm{L}^{-3}

    Correct
  3. Option C:

    The dimension of power is L−5\mathrm{L}^{-5}

  4. Option D:

    The dimension of linear momentum is L−1\mathrm{L}^{-1}

    Correct

Answer: A, B, D

Step-by-step solution

[M0 L0 T0]=[ML2 T−1]\left[\mathrm{M}^{0} \mathrm{~L}^{0} \mathrm{~T}^{0}\right]=\left[\mathrm{ML}^{2} \mathrm{~T}^{-1}\right]

⇒[L2]=[T]\Rightarrow\left[\mathrm{L}^{2}\right]=[\mathrm{T}]

Energy =[MLT−2L]=L−2=\left[M L T^{-2} L\right]=L^{-2}

Force =[MLT−2]=L−3=\left[\mathrm{MLT}^{-2}\right]=\mathrm{L}^{-3}

Power =[MLT−2LT−1]=L−4=\left[\mathrm{MLT}^{-2} \mathrm{LT}^{-1}\right]=\mathrm{L}^{-4}

linear momentum =MLT−1=L−1=\mathrm{MLT}^{-1}=\mathrm{L}^{-1}

Answer key and solution verified before publishing.

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Exam
JEE Advanced 2019
Paper
Paper 1
Subject
Physics
Chapter
Units, Dimensions & Error Analysis
Topic
Units and Dimensions Analysis
Let us consider a system of units in which mass and angular momentum… | JEE Advanced 2019 PYQ with Solution · DhiX AI