If the units of force, energy and velocity are $10$ N, $100$ J and $5$ m/s then the unit of mass is :

1 kg

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2 kg

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3 kg

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4 kg

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Solution

The correct option is D 4 kg
$F o r c e = [M^{1} L^{1} T^{- 2}] = F$
$E n e r g y = [M^{1} L^{2} T^{- 2}] = E$
$V e l o c i t y = [L T^{- 1}] = V$
$M^{1} α F^{a} E^{b} V^{c}$
$M^{'} = {(M^{1} L^{1} T^{- 2})}^{a} {(M^{1} L^{2} T^{- 2})}^{b} {(L T^{- 1})}^{c}$
$1 = a + b : b + c = - 1 : c = - 2$
$0 = a + 2 b + c : - (2 a + 2 b) - c = 0 : b = 1$
$0 = - 2 a - 2 b - c : a = 0$
$\Rightarrow M a s s = \frac{E n e r g y}{{(V e l o c i t y)}^{2}} = \frac{100}{{(5)}^{2}} = 4 k g$

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