Question

Let us assume that the acceleration due to gravity be $10m/s^2$. If acceleration due to gravity ($g$), the velocity ($v$) acquired by a body after falling from rest for $5$ seconds and the momentum ($p$) acquired by a mass of $1$ kg in falling freely from rest for $10$ seconds are taken as the fundamental units, then the value of the unit of mass in terms of kg ?

• A. 1 kg
• B. 2 kg
• C. 5 kg
• D. 10 kg

Answer 1

Answer: (B)

2 kg

$g=10\frac{m}{s^2}$
$v=u+gt=5g\frac{m}{s}$
$p=momentumfor1kg=m{v}_1=m(0+10g)=10mg$

$M^{\prime }=g^{\alpha }{v}^{\beta }{p}^{\gamma }$
$M^1{L}^0{T}^0={\left(L{T}^{-2}\right)}^{\alpha }{\left(L{T}^{-1}\right)}^{\beta }{\left(M^1{L}^1{T}^{-1}\right)}^{\gamma }$
$\gamma =1,\alpha +\beta +\gamma =0,-2\alpha -\beta -\gamma =0$
$\alpha +\beta =-1$
$-2\gamma -\beta =1$

$-\alpha =0$
$\beta =-1$
$\gamma =1$
$M^{\prime }=\frac{P}{V}=\frac{10g}{5g}=2kg$