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Questions  

If the velocity (V), acceleration (A), and force (F) are taken as fundamental quantities instead of mass (M) length (L), and time (T), the dimensions of Young's modulus (Y) would be

a
FA2V−4
b
FA2V−5
c
FA2V−3
d
FA2V−2

detailed solution

Correct option is A

Let Y=VaAbFc ML−1T−2=LT−1aLT−2bMLT−2c ML−1T−2=McLa+b+cT−a−2b−2c∴ c=1,a+b+c=−1,−a−2b−2c=−2 On solving, we get a=−4,b=2, and c=1.

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