Consider Law of Homogeniety of Dimensions. Now, choose the correct option:
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a
T2=4π2r3GM
b
T2=4π2r2
c
T2=4π2r3G
d
T=4π2r3G
answer is A.
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Detailed Solution
T2=4π2r3GMTaking dimensions on both ides, we get[T]2=[L]3M−1L3T−2M=M0L0T2∴LHS=RHS Now, T2=4π2r2Taking dimensions on both sides[T]2=[L]2∴LHS≠RHS Now, T2=4π2r3CTaking dimensions on both sides[T]2=L3M−1L3T2M1L0T−1∴LHS≠RHS Now, T=4π2r3G[T]=L3M−1L3T−2=ML0T2∴LHS≠RHS