JEE Main · 2025 · 28 Jan 2025 · Shift 1 · Units & Measurement

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In a measurement, it is asked to find modulus of elasticity per unit torque applied on the system. The measured quantity has dimension of

[M^{a} L^{b} T^{c}]

. If

b = 3

, the value of

c

____

Answer: 0

Solution

Consider the quantity formed from modulus of elasticity and torque. Modulus of elasticity carries the dimensions of stress,

[Modulus] = \frac{[ Force ]}{[ Area ]} = [M L^{- 1} T^{- 2}]

while torque has the dimensions of force times length,

[Torque] = [M L^{2} T^{- 2}]

Their ratio gives

\frac{[ Modulus ]}{[ Torque ]} = \frac{[ M L ^{- 1} T ^{- 2} ]}{[ M L ^{2} T ^{- 2} ]} = [M^{0} L^{- 3} T^{0}]

This combination carries no dependence on mass or time. Whether the measured quantity is taken as modulus per unit torque (giving a length exponent of

- 3

) or its reciprocal, torque per unit modulus of elasticity (giving a length exponent of

+ 3

, matching

b = 3

as stated in the problem), the time exponent is unaffected either way:

c = 0

JEE Main · 2025 · 28 Jan 2025 · Shift 1 · Integer answer

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JEE Main · 2025 · 28 Jan 2025 · Shift 1 · Units & Measurement

Solution

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