Physics

Which of the following pair have same dimensional formula for both the quantities?
i) kinetic energy and torque
ii)  resistance and inductance
iii)  Young's modulus and pressure


ANSWER

All the three


SOLUTION
Dimension's of :

$$(a)\ K.E=[M^{1} L^{2} T^{-2}]$$

Torque $$=[M^{1} L^{2} T^{2}]$$

$$(b)$$ Resistance $$=[M^{-1} L^{2} T^{-3} A^{-2}]$$

Inductance $$=[M^{1} L^{2} T^{3} A^{-2}]$$

$$(c)$$ Young's Modulus. $$E=[M^{1} L^{-1} T^{-2}]$$

Pressure; $$P=\dfrac {[Force]}{Area}$$

$$=\dfrac {[M^1 L^1 T^{-2}]}{[L^2]} $$

$$=[M^1 L^1 T^{-2}]$$

$$=[M^1 L^{-1} T^{-2}]$$

$$\therefore \ $$ All the $$3$$ have same Dimensional formula.
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