The units of force, velocity and energy are 100 dyne, 10 ${c m s}^{- 1}$ and 500 erg respectively. The units of mass, length and time are:

5 g, 5 cm, 5 s

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5 g, 5 cm, 0.5 s

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0.5 g, 5 cm, 5 s

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5 g, 0.5cm, 5 s

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Solution

The correct option is C 5 g, 5 cm, 0.5 s
Force $= 100 d y n e = M^{1} L^{1} T^{- 2}$
$v e l o c i t y = 10 \frac{c m}{s} = L T^{- 1}$
$E n e r g y = 500 e r g = M^{1} L^{2} T^{- 2} \Rightarrow \frac{e n e r g y}{f o r c e} = L^{1} = \frac{500}{100} = 5 c m$
$\Rightarrow \frac{e n e r g y}{(v e l o c i t y)^{2}} = M^{1} = \frac{500}{(10)^{2}} = 5 g m \Rightarrow T = 0.5 s e c$

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The units of force, velocity and energy are 100 dyne, 10 cms−1 and 500 erg respectively. The units of mass, length and time are:

The correct option is C 5 g, 5 cm, 0.5 sForce =100dyne=M1L1T−2velocity=10cms=LT−1Energy=500erg=M1L2T−2⇒energyforce=L1=500100=5cm⇒energy(velocity)2=M1=500(10)2=5gm⇒T=0.5 sec

The units of force, velocity and energy are 100 dyne, 10 ${c m s}^{- 1}$ and 500 erg respectively. The units of mass, length and time are: