মাত্রা ও একক বিষয়ক

Match the physical quantities given in Column I ;with suitable dimensions expressed in Column& ;II.

Column IColumn II
a) Angular momentum1) M−1L3T−2{ M }^{ -1 }{ L }^{ 3 }{ T }^{ -2 }
b) Torque2) MLT−2{ MLT }^{ -2 }
c) Gravitational constant3) ML2T−2{ ML }^{ 2 }{ T }^{ -2 }
d) Tension 4) ML2T−1{ ML }^{ 2 }{ T }^{ -1 }

হানি নাটস

Angular momentum is given by L⃗=r⃗×p⃗\vec L =\vec r \times \vec p.

Thus, it's dimensions are [L]=L.MLT−1=ML2T−1[L]=L.MLT^{-1}=ML^{2}T^{-1}

Torque is given as r⃗×F⃗\vec r \times \vec F.

Thus, dimensions are L.MLT−2=ML2T−2L.MLT^{-2}=ML^2T^{-2}.

Tension is force and hence its dimensions are MLT−2MLT^{-2}.

Gravitational constant relationship is F=GMmr2F=G\dfrac{Mm}{r^2}

Thus, [G]=[F][r2][Mm]=MLT−2.L2M2=M−1L3T−2[G]=\dfrac{[F][r^2]}{[Mm]}=\dfrac{MLT^{-2}.L^2}{M^2}=M^{-1}L^3T^{-2}

Thus, option C is correct.

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