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Match the physical quantities in column A with their dimensional formula expressed in column B
`{:(Column A,, ColumnB),((1) "Anguar Momentum",,(a)ML^(2)T^(-2)),((2)"Latent Heat",,(b)ML^(2)T^(-2)A^(-2)),((3)"Torque",,(c)ML^(2)T^(-1)),((4)"Capacitance",,(d)ML^(3)T^(-3)A^(-2)),((5)"Inductance",,(e)M^(-1)L^(-2)T^(4)A^(2)),("(Resistivity",,(f)ML^(2)T^(-2)A^(-1)),((7)"Magnetic",,(g)ML^(-1)T^(-2)),((8)"Magnetic",,(h)L^(2)T^(-2)):}`

Text Solution

Verified by Experts

The correct Answer is:
`[1-(c), 2-(h), 3-(a), 4-(e), 5-(b), 6-(d), 7-(f), 8-(g)]`

(1) `[l]=[mvr]=(MLT^(_1)L)`
(2) `"Latent heat":Q=ML`
`[Q]=[M][L] rArr [L]=(ML^(2)T^(-2))/(M)=L^(2)T^(-2)`
(3) `["Torque"]=[r][F] " " (vec(tau)=vec(r)xxvec(F))`
`[tau]=L.MLT^(-2)`
`[tau]=ML^(2)T^(-2)`
(4) Capacitance
`C=(q)/(V)=(q.q)/(U)`
`C=q^(2)/(V) " " (.:V=(V)/(q))`
`rArr [C]=A^(2)T^(2)xx(ML^(2)T^(-2))^(-1)=M^(-1)L^(-2)T^(4)A^(2)`
(5) Inductance
`phi=Li "&" E=-(dphi)/(dt)`
`[L]=([V][t])/([i])=([U])/[[q]).(T)/(A)=(ML^(2)T^(-2).T)/(AT.A)`
`[L]=ML^(2)T^(-2)A^(-2)`
(6) `R=(rhol)/(A) rArr [rho]=[(V)/(i)].(L^(2))/(L)=(ML^(2)T^(-2))/(AT.A).L`
`[R]=ML^(3)T^(-3)A^(-2)`
(7) `phi=BAcos theta & F=qVB sin theta`
`[phi]=[(F)/(qv)][A]=ML^(2)T^(-2)A^(-1)`
(8) `u=(B^(2))/(4mu_(0))`
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