PRINCIPLE OF HOMOGENEITY
Units and Measurements

269192 SI unit and C G S unit of a quantity vary by\(10^{7}\) times, it is

1 Boltzmann'sconstant
2 Gravitationa constant
3 Planck's constant
4 Angular momentum
Units and Measurements

269193 The initial velocity of a particle is given by\(u^{2}=v^{2}-2 g x\) where \(\boldsymbol{x}\) is the distance covered. If \(\mathbf{u}=\mathbf{1 8} \mathrm{km} \mathrm{h}^{-1}, \mathbf{g}=\mathbf{1 0 0 0} \mathrm{cm} / \mathrm{s}^{2} \boldsymbol{x}\) \(=150 \mathrm{~cm}\) then \(\mathrm{v}=\) ----_ \(\mathbf{m} / \mathrm{s}\)

1 \(\sqrt{45}\)
2 \(\sqrt{55}\)
3 \(\sqrt{35}\)
4 \(\sqrt{65}\)
Units and Measurements

269194 Theequation which is dimensionally correct among the following is

1 \(v=u+\frac{1}{2} a t\)
2 \(v=u t+a t\)
3 \(s=ut+a t^{3}\)
4 \(t=s+a v\)
Units and Measurements

269195 The dimensions of\(\gamma\) in the relation \(v=\sqrt{\frac{\gamma p}{\rho}}\) (where \(v\) is velocity, \(\mathbf{p}\) is pressure, \(\rho\) is density)

1 Dimensionless
2 \(\left[L T^{-1}\right]\)
3 \(\left[M L^{-1} T^{-2}\right]\)
4 \(\left[M L^{-3}\right]\)
Units and Measurements

269192 SI unit and C G S unit of a quantity vary by\(10^{7}\) times, it is

1 Boltzmann'sconstant
2 Gravitationa constant
3 Planck's constant
4 Angular momentum
Units and Measurements

269193 The initial velocity of a particle is given by\(u^{2}=v^{2}-2 g x\) where \(\boldsymbol{x}\) is the distance covered. If \(\mathbf{u}=\mathbf{1 8} \mathrm{km} \mathrm{h}^{-1}, \mathbf{g}=\mathbf{1 0 0 0} \mathrm{cm} / \mathrm{s}^{2} \boldsymbol{x}\) \(=150 \mathrm{~cm}\) then \(\mathrm{v}=\) ----_ \(\mathbf{m} / \mathrm{s}\)

1 \(\sqrt{45}\)
2 \(\sqrt{55}\)
3 \(\sqrt{35}\)
4 \(\sqrt{65}\)
Units and Measurements

269194 Theequation which is dimensionally correct among the following is

1 \(v=u+\frac{1}{2} a t\)
2 \(v=u t+a t\)
3 \(s=ut+a t^{3}\)
4 \(t=s+a v\)
Units and Measurements

269195 The dimensions of\(\gamma\) in the relation \(v=\sqrt{\frac{\gamma p}{\rho}}\) (where \(v\) is velocity, \(\mathbf{p}\) is pressure, \(\rho\) is density)

1 Dimensionless
2 \(\left[L T^{-1}\right]\)
3 \(\left[M L^{-1} T^{-2}\right]\)
4 \(\left[M L^{-3}\right]\)
Units and Measurements

269192 SI unit and C G S unit of a quantity vary by\(10^{7}\) times, it is

1 Boltzmann'sconstant
2 Gravitationa constant
3 Planck's constant
4 Angular momentum
Units and Measurements

269193 The initial velocity of a particle is given by\(u^{2}=v^{2}-2 g x\) where \(\boldsymbol{x}\) is the distance covered. If \(\mathbf{u}=\mathbf{1 8} \mathrm{km} \mathrm{h}^{-1}, \mathbf{g}=\mathbf{1 0 0 0} \mathrm{cm} / \mathrm{s}^{2} \boldsymbol{x}\) \(=150 \mathrm{~cm}\) then \(\mathrm{v}=\) ----_ \(\mathbf{m} / \mathrm{s}\)

1 \(\sqrt{45}\)
2 \(\sqrt{55}\)
3 \(\sqrt{35}\)
4 \(\sqrt{65}\)
Units and Measurements

269194 Theequation which is dimensionally correct among the following is

1 \(v=u+\frac{1}{2} a t\)
2 \(v=u t+a t\)
3 \(s=ut+a t^{3}\)
4 \(t=s+a v\)
Units and Measurements

269195 The dimensions of\(\gamma\) in the relation \(v=\sqrt{\frac{\gamma p}{\rho}}\) (where \(v\) is velocity, \(\mathbf{p}\) is pressure, \(\rho\) is density)

1 Dimensionless
2 \(\left[L T^{-1}\right]\)
3 \(\left[M L^{-1} T^{-2}\right]\)
4 \(\left[M L^{-3}\right]\)
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Units and Measurements

269192 SI unit and C G S unit of a quantity vary by\(10^{7}\) times, it is

1 Boltzmann'sconstant
2 Gravitationa constant
3 Planck's constant
4 Angular momentum
Units and Measurements

269193 The initial velocity of a particle is given by\(u^{2}=v^{2}-2 g x\) where \(\boldsymbol{x}\) is the distance covered. If \(\mathbf{u}=\mathbf{1 8} \mathrm{km} \mathrm{h}^{-1}, \mathbf{g}=\mathbf{1 0 0 0} \mathrm{cm} / \mathrm{s}^{2} \boldsymbol{x}\) \(=150 \mathrm{~cm}\) then \(\mathrm{v}=\) ----_ \(\mathbf{m} / \mathrm{s}\)

1 \(\sqrt{45}\)
2 \(\sqrt{55}\)
3 \(\sqrt{35}\)
4 \(\sqrt{65}\)
Units and Measurements

269194 Theequation which is dimensionally correct among the following is

1 \(v=u+\frac{1}{2} a t\)
2 \(v=u t+a t\)
3 \(s=ut+a t^{3}\)
4 \(t=s+a v\)
Units and Measurements

269195 The dimensions of\(\gamma\) in the relation \(v=\sqrt{\frac{\gamma p}{\rho}}\) (where \(v\) is velocity, \(\mathbf{p}\) is pressure, \(\rho\) is density)

1 Dimensionless
2 \(\left[L T^{-1}\right]\)
3 \(\left[M L^{-1} T^{-2}\right]\)
4 \(\left[M L^{-3}\right]\)