Units & Dimensions

JEE Main level, numerical answer, medium

47 of 149

Question 47 of 149

In a measurement, it is asked to find modulus of elasticity per unit torque applied on the system. The measured quantity has dimension of [MaLbTc]\left[M^a L^b T^c\right]. If b=−3b=-3, the value of cc is ________

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Answer: 0

[Modulus of elasticity] =ML−1 T−2=\mathrm{ML}^{-1} \mathrm{~T}^{-2}
[Torque] == ML 2 T−2^2 \mathrm{~T}^{-2}
[Modulus of elasticity per unit torque]
=ML−1 T−2ML2 T−2=L−3=\frac{\mathrm{ML}^{-1} \mathrm{~T}^{-2}}{\mathrm{ML}^2 \mathrm{~T}^{-2}}=\mathrm{L}^{-3}

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