JEE Advanced · 2019 · 27 May 2019 · Paper 1 · Units & Measurement

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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 ?

(A)The dimension of force is $L^{- 3}$ ✓ Correct
(B)The dimension of energy is $L^{- 2}$ ✓ Correct
(C)The dimension of power is $L^{- 5}$
(D)The dimension of linear momentum is $L^{- 1}$ ✓ Correct

Answer: (A), (B), (D)

Solution

Given: Mass

= M^{0} L^{0} T^{0}

(dimensionless)

Angular momentum

M V r = M^{0} L^{0} T^{0}

M^{0} \frac{L ^{1}}{T ^{1}} \cdot L^{1} = M^{0} L^{0} T^{0}

L^{2} = T^{1}

Force: In SI,

[F] = M^{1} L^{1} T^{- 2}

In new system:

[F] = M^{0} L^{1} L^{- 4} = L^{- 3}

✓

Energy: In SI,

[E] = M^{1} L^{2} T^{- 2}

In new system:

[E] = M^{0} L^{2} L^{- 4} = L^{- 2}

✓

Power: In SI,

[P] = M^{1} L^{2} T^{- 3}

In new system:

[P] = M^{0} L^{2} L^{- 6} = L^{- 4}

✗

Linear momentum: In SI,

[p] = M^{1} L^{1} T^{- 1}

In new system:

[p] = M^{0} L^{1} L^{- 2} = L^{- 1}

✓

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JEE Advanced · 2019 · 27 May 2019 · Paper 1 · Units & Measurement

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