JEE MAIN - Physics (2021 - 26th February Evening Shift - No. 6)
If 'C' and 'V' represent capacity and voltage respectively then what are the dimensions of $$\lambda$$ where C/V = $$\lambda$$ ?
$$[{M^{ - 3}}{L^{ - 4}}{I^3}{T^7}]$$
$$[{M^{ - 2}}{L^{ - 3}}{I^2}{T^6}]$$
$$[{M^{ - 2}}{L^{ - 4}}{I^3}{T^7}]$$
$$[{M^{ - 1}}{L^{ - 3}}{I^{ - 2}}{T^{ - 7}}]$$
Explanation
$$\lambda = {C \over V} = {{Q/V} \over V} = {Q \over {{V^2}}}$$
$$V = {{work} \over Q}$$
$$\lambda = {{{Q^3}} \over {{{(work)}^2}}} = {{{{(It)}^3}} \over {{{(F.s)}^2}}}$$
$$ = {{\left[ {{I^3}{T^3}} \right]} \over {{{\left[ {M{L^2}{T^{ - 2}}} \right]}^2}}} = [{M^{ - 2}}{L^{ - 4}}{I^3}{T^7}]$$
$$V = {{work} \over Q}$$
$$\lambda = {{{Q^3}} \over {{{(work)}^2}}} = {{{{(It)}^3}} \over {{{(F.s)}^2}}}$$
$$ = {{\left[ {{I^3}{T^3}} \right]} \over {{{\left[ {M{L^2}{T^{ - 2}}} \right]}^2}}} = [{M^{ - 2}}{L^{ - 4}}{I^3}{T^7}]$$
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